Carnegie Learning Math Series Volume 1 4th Edition Chapter 1 Linear Equations
Carnegie Learning Math Series Volume 14th Edition Chapter 1 Exercise 1.3 Solution Page 26 Problem 1 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry, and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We have to define a variable for the number of DVDs that Dan has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Hence, we have assigned the variable x for the number of DVDs that Dan has.
Page 26 Problem 2 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We have to write and solve algebraic equations to find out the number of DVDs that Donna has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Now, let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Hence, if the number of DVDs that Dan has is x, then the number of DVDs that Donna will have is x + 7.
We can substitute any value against x and then we can find the number of DVDs that Dan and Donna own.
Page 26 Problem 3 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We have to write and solve algebraic equations to find out the number of DVDs that Betty has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has= 2 × (x + 7)
= 2x + 14
If the number of DVDs that Dan has is x, then the number of DVDs that Donna will have is x + 7.
Hence, the number of DVDs that Betty will have is 2x + 14.
We can substitute any value against x and then we can find the number of DVDs that Dan, Donna, and Betty own.
Solutions For Linear Equations Exercise 1.3 In Carnegie Learning Math Series Page 26 Problem 4 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry, and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We have to write and solve algebraic equations to find out the number of DVDs that Jerry has.
Let us find out about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Now, let us find out about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Hence, if the number of DVDs that Dan has is x, then the number of DVDs that Jerry will have is 3x.
We can substitute any value against x and then we can find the number of DVDs that Dan and Jerry own.
Page 26 Problem 5 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We have to write and solve algebraic equations to find out the number of DVDs that Kenesha has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has = (x + 7) − 6
= x + 1
If the number of DVDs that Dan has is x, then the number of DVDs that Donna will have is x + 7.
Hence, the number of DVDs that Kenesha will have is x + 1.
We can substitute any value against x and then we can find the number of DVDs that Dan, Donna, and Kenesha own.
Carnegie Learning Math Series 4th Edition Exercise 1.3 Solutions Page 26 Problem 6 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We are given that the friends have a total of 182 DVDs altogether.
We have to write and solve algebraic equations to find out the number of DVDs that Dan has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has = 2 × (x + 7)
= 2x + 14
Now, let us find about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has = (x + 7) − 6
= x + 1
We are given that the total number of DVDs that the friends own = 182
Then, the linear equation that will be made is,
⇒ x + (x + 7) + (2x + 14) + 3x + (x + 1) = 182
⇒ 8x + 22 = 182
Now, we will solve this linear equation.
⇒ 8x + 22 = 182
Transporting 22 on the right side,
⇒ 8x = 182 − 22
⇒ 8x = 160
Transporting 8 on the right side,
⇒ x = 160/8
⇒ x = 20
We assigned the variable x to the number of DVDs that Dan has and now we have found out its value.
Hence, the number of DVDs that Dan has is 20.
Page 26 Problem 7 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry, and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We are given that the friends have a total of 182 DVDs altogether.
We have to write and solve algebraic equations to find out the number of DVDs that Donna has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has = 2 × (x + 7)
= 2x + 14
Now, let us find about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has = (x + 7) − 6
= x + 1
We are given that the total number of DVDs that the friends own = 182
Then, the linear equation that will be made is,
⇒ x + (x + 7) + (2x + 14) + 3x + (x + 1) = 182
⇒ 8x + 22 = 182
Now, we will solve this linear equation.
⇒ 8x + 22 = 182
Transporting 22 on the right side,
⇒ 8x = 182 − 22
⇒ 8x = 160
Transporting 8 on the right side,
⇒ x = 160/8
⇒ x = 20
So, Dan owns 20 DVDs.
We have to find out how many DVDs Donna owns.
The algebraic expression that shows the number of DVDs Donna has is x + 7.
Substituting the value of x,
= 20 + 7
= 27
The number of DVDs that Donna owns is 27.
Linear Equations Solutions Chapter 1 Exercise 1.3 Carnegie Learning Math Series Page 26 Problem 8 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We are given that the friends have a total of 182 DVDs altogether.
We have to write and solve algebraic equations to find out the number of DVDs that Betty has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has = 2 × (x + 7)
= 2x + 14
Now, let us find about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has= (x + 7) − 6
= x + 1
We are given that the total number of DVDs that the friends own = 182
Then, the linear equation that will be made is,
⇒ x + (x + 7) + (2x + 14) + 3x + (x + 1) = 182
⇒ 8x + 22 = 182
Now, we will solve this linear equation.
⇒ 8x + 22 = 182
Transporting 22 on the right side,
⇒ 8x = 182 − 22
⇒ 8x = 160
Transporting 8 on the right side,
⇒ x = 160/8
⇒ x = 20
So, Dan owns 20 DVDs.
We have to find out how many DVDs Betty owns.
The algebraic expression that shows the number of DVDs Betty has is 2x + 14.
Substituting the value of x,
= (2 × 20) + 14
= 40 + 14
= 54
The number of DVDs that Betty owns is 54.
Step-By-Step Solutions For Carnegie Learning Math Series Chapter 1 Exercise 1.3 Page 26 Problem 9 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We are given that the friends have a total of 182 DVDs altogether.
We have to write and solve algebraic equations to find out the number of DVDs that Jerry has.
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has = 2 × (x + 7)
= 2x + 14
Now, let us find about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has = (x + 7) − 6
= x + 1
We are given that the total number of DVDs that the friends own = 182
Then, the linear equation that will be made is,
⇒ x + (x + 7) + (2x + 14) + 3x + (x + 1) = 182
⇒ 8x + 22 = 182
Now, we will solve this linear equation.
⇒ 8x + 22 = 182
Transporting 22 on the right side,
⇒ 8x = 182 − 22
⇒ 8x = 160
Transporting 8 on the right side,
⇒ x = 160/8
⇒ x = 20
So, Dan owns 20 DVDs.
We have to find out how many DVDs Jerry owns.
The algebraic expression that shows the number of DVDs Jerry has is 3x.
Substituting the value of x,
= 3 × 20
= 60
The number of DVDs that Jerry owns is 60.
Page 26 Problem 10 Answer
We are given conditions about the number of DVDs five friends – Dan, Donna, Betty, Jerry and Kenesha have.
Dan has the fewest.
Donna has 7 more than Dan.
Betty has twice as many as Donna.
Jerry has 3 times as many as Dan.
Kenesha has 6 less than Donna.
We are given that the friends have a total of 182 DVDs altogether.
We have to write and solve algebraic equations to find out the number of DVDs that Kenesha
Let us find about the number of DVDs that Dan possesses.
We are given that Dan has the fewest number of DVDs.
Let the variable for the number of DVDs that Dan has be x.
Let us find about the number of DVDs that Donna possesses.
She has 7 more of them than Dan has.
We can say that the number of DVDs that Donna has = x + 7
Now, let us find about the number of DVDs that Betty possesses.
She has twice as many as Donna.
So, we can say that the number of DVDs that Betty has = 2 × (x + 7)= 2x + 14
Now, let us find about the number of DVDs that Jerry possesses.
Jerry has 3 times as many of them as Dan.
So, we can say that the number of DVDs that Jerry has = 3x
Now, let us find about the number of DVDs that Kenesha possesses.
She has 6 fewer of them than Donna.
So, we can say that the number of DVDs that Kenesha has = (x + 7) − 6= x + 1
We are given that the total number of DVDs that the friends own = 182
Then, the linear equation that will be made is,
⇒ x + (x + 7) + (2x + 14) + 3x + (x + 1) = 182
⇒ 8x + 22 = 182
Now, we will solve this linear equation.
⇒ 8x + 22 = 182
Transporting 22 on the right side,
⇒ 8x = 182 − 22
⇒ 8x = 160
Transporting 8 on the right side,
⇒ x = 160/8
⇒ x = 20
So, Dan owns 20 DVDs.
We have to find out how many DVDs Kenesha owns.
The algebraic expression that shows the number of DVDs Kenesha has is x + 1.
Substituting the value of x,
= 20 + 1
= 21
The number of DVDs that Kenesha owns is 21.
Page 27 Problem 11 Answer
Given: The number of DVDs owned by five friends.
Donna says the sum of DVDs with Donna and Kenesha is equal to DVDs with Betty.
To write and solve algebraic expressions to state that Donna’s claim is wrong.
Let the number of DVDs owned by Dan be x
Donna has 7 more than Dan, so the expression will be ⇒7+x
Betty has twice as many as Donna, so the expression will be
⇒2(7+x)
⇒2x+14
Herry has 3 times as many as Dan, so the expression will be ⇒3x
Kenesha has 6 less than Donna, so the expression will be
⇒(7+x)−6
⇒x+1
According to Donna,
DVDs with Donna+DVDs with Kanesha=DVDs with Betty
⇒DVDs with Donna+DVDs with Kanesha=(7+x)+(x+1)
⇒2x+8
⇒DVDs with Betty=2x+14
So Donna’s reasoning is incorrect.
Sum of DVDs with Donna and Kenesha≠
DVDs with Betty
So, Donna’s statement is wrong.
Carnegie Learning Math Series Exercise 1.3 Student Solutions Page 27 Problem 12 Answer
Given: The money raised by club members for a club trip
To define a variable for the amount raised by Harry
Since the amount raised by Harry is unknown,
Let it be defined as x
The amount raised by Harry is defined as x.
Page 28 Problem 13 Answer
Given: The money raised by club members for a club trip
Henry raised $7.50 less than Harry
To write an algebraic expression for the money raised by Henry.
The amount raised by Harry is x
Henry raised $7.50 less than Harry
⇒Amount raised by Henry=x−7.50
The expression for the amount raised by Henry is x−7.50
Page 28 Problem 14 Answer
Given: The money raised by club members for a club trip
Helen raised twice as much as Henry.
To write an algebraic expression for the money raised by Helen.
The expression for the amount raised by Henry is x−7.5
Helen had raised twice as much as Henry.
⇒ Amount raised by Helen=2(x−7.5)
⇒2x−15
The expression for the amount raised by Helen is 2x−15
Page 28 Problem 15 Answer
Given: The money raised by club members for a club trip
Heddy raised a third as much as Helen.
To write an algebraic expression for the money raised by Heddy.
The expression for the amount raised by Helen is 2x−15
Heddy had raised a third as much as Helen.
⇒ Amount raised by Heddy=1/3(2x−15)
⇒2/3x−5
The expression for the amount raised by Heddy is 2/3x−5
Page 28 Problem 16 Answer
Given: The money raised by club members for a club trip
Hailey raised $4 less than 3 times as much as Helen.
To write an algebraic expression for the money raised by Hailey.
The expression for the amount raised by Helen is 2x−15
Hailey raised $4 less than 3 times as much as Helen.
⇒ Amount raised by Hailey=3(2x−15)−4
⇒6x−45−4
⇒6x−49
The expression for the amount raised by Hailey is 6x−49
Page 28 Problem 17 Answer
Given: The money raised by club members for a club trip
Amount raised by Harry is $55
To find the amount raised by Henry
The amount raised by Harry,x=55
So Amount raised by Henry=x−7.5
⇒55−7.5=47.5
The amount raised by Henry is $47.5
Page 28 Problem 18 Answer
Given: The money raised by club members for a club trip
The amount raised by Harry is $55
To find the amount raised by Helen
Amount raised by Harry,x=55
⇒ Amount raised by Helen=2x−15
⇒(2×55)−15=95
The amount raised by Helen is $95
Page 28 Problem 19 Answer
Given: The money raised by club members for a club trip
Amount raised by Harry is $55
To find the amount raised by Heddy
Amount raised by Harry,x=55
⇒ Amount raised by Heddy=2/3x−5
⇒(2/3×55)−5=31.67
The amount raised by Heddy is $31.67
Page 28 Problem 20 Answer
Given: The money raised by club members for a club trip
Amount raised by Harry is $55
To find the amount raised by Hailey
Amount raised by Harry,x=55
⇒ Amount raised by Hailey=6x−49
⇒(6×55)−49=281
The amount raised by Hailey is $281
Linear Equations Exercise 1.3 Carnegie Learning 4th Edition Answers Page 28 Problem 21 Answer
Given: The money raised by club members for a club trip
Amount raised by Heddy is $40
To find the amount raised by Harry
Amount raised by Heddy= $40
The expression for the amount raised by Heddy is 2/3x−5
Equating both the expression to solve for x
⇒2/3x−5=40
Adding 5 on both sides
⇒2/3x−5+5=40+5
⇒2/3x=45
Multiplying 3 on both sides
⇒2/3x×3=45×3
⇒2x=135
Dividing 2 on both sides
⇒2x/2=135/2
⇒x=67.5
Since x is the amount raised by Harry, he earned $67.50
The amount raised by Harry is $67.50
Page 28 Problem 22 Answer
Here, we are given the amount raised by Heddy as $40
and we have to determine the amount of money raised by Henry. So, we will proceed as follows:
We had determined the expression for the amount of money raised by Heddy as 2/3(x−7.5).
We will set this expression equal to $40 as per the question and determine the value of the variablex.
Then, we will substitute the value of x in the expression for the amount of money raised by Henry, which we found as(x−7.5).
Thus, we will get the required amount.
So, as per the question, we the amount raised by Heddy as $40.
Now, setting the expression for the amount raised by Heddy equal to40,
we get
⇒2/3(x−7.5)=40
Multiplying by 3 each side as per the multiplication property of equality, we get
⇒3×2/3(x−7.5)=40×3
⇒2(x−7.5)=120
Dividing by 2 each side as per the division property of equality, we get
⇒2/2(x−7.5)=120/2
⇒x−7.5=60 (Simplifying)
Adding7.5 each side as per the addition property of equality, we get
⇒x−7.5+7.5=60+7.5
⇒x=67.5
So, the amount of money raised by Heddy is $67.5.
Now, we have the expression for the amount of money raised by Henry as follows:
⇒x−7.5
Substituting the value of x=67.5 as found in the previous step, we get
⇒67.5−7.5
⇒60
So, the amount of money raised by Henry is $60.
The amount of money raised by Henry is found as $60.
Page 28 Problem 23 Answer
Here, we have to find the amount of money raised by Helen.
We determined the value of the variable x in the previous part as 60.
Now, we will substitute this value in the expression for the amount of money raised by Helen which is given as2(x−7.5) and determine the required amount.
So, we write the expression for the amount raised by Helen as follows:
⇒2(x−7.5)
Substitutingx=60 as found in the previous part, we get
⇒2(67.5−7.5)
⇒2(60)
⇒120
So, the amount raised by Helen is $120.
The amount of money raised by Helen is $120.
Page 28 Problem 24 Answer
Here, we have to find the amount of money raised by Hailey.
We have determined the value of the variable x in the previous part as67.5.
We will substitute this value in the expression for the amount raised by Hailey given as2(x−7.5)−4.
So, we write the expression for the amount raised by Hailey as follows:
⇒2(x−7.5)−4
Substitutingx=67.5, we get
⇒2(67.5−7.5)−4
⇒2(60)−4
⇒120−4
⇒116
So, the required amount is $116.
The amount of money raised by Hailey is found as $116.
Page 29 Problem 25 Answer
Here, we are given the amount of money raised by Henry, Helen, and Hailey altogether as $828.50.
We have to find the amount of money raised by Harry. So, we will proceed as follows:
We had found the expressions for the amount of money raised by Henry, Helen and Hailey.
We will add these expressions and set them equal to 828.50 as per the question and solve for the value of x.
This value of x will be the amount of money raised by Harry as we assumed in the previous parts.
So, we have the expressions for the amount of money raised as:
Amount raised by Harry=x
Amount raised by Henry=x−7.5
Amount raised by Helen=2(x−7.5)
Amount raised by Hailey=2(x−7.5)−4
As per the question, we have the condition as Henry, Helen, and Hailey raised $828.50 altogether.
So, we have the equation as follows:
⇒(x−7.5)+2(x−7.5)+2(x−7.5)−4=828.50
⇒x−7.5+2x−14+2x−14−4=828.50
⇒x+2x+2x−7.5−7.5−14−4=828.50
⇒5x−14−14−4=828.50
⇒5x−24=828.50
Adding24 each side, we get
⇒5x−24+24=828.50+24
⇒5x=852.5
Dividing by 5 each side, we get
⇒5x/5
=852.5/5
⇒x=170.5
So, the required amount is $170.5.
The amount of money raised by Harry is found as $170.5.
Page 29 Problem 26 Answer
Here, we have to find the amount of money raised by Henry.
We have the expression representing this as x−7.5.
We will substitute the value of x as found in the previous part and get the required amount.
So, we write the expression for the amount of money raised by Henry as follows:
⇒x−7.5
Substituting the value of x=170.5 as found in the previous part, we get
⇒170.5−7.5
⇒163
So, the amount of money raised by Henry is $163.
The amount of money raised by Henry is found as $163.
Page 29 Problem 27 Answer
Here, we have to find the amount of money raised by Helen.
We have the expression representing this as 2(x−7.5).
We will substitute the value of x as found in the previous part and get the required amount.
So, we write the expression for the amount of money raised by Helen as:
⇒2(x−7.5)
Substitutingx=170.5
as found in the part (a), we get
⇒2(170.5−7.5)
⇒2(163)
⇒326
So, the amount of money raised by Helen is $326.
The amount of money raised by Helen is found as $326.
Page 29 Problem 28 Answer
Here, we have to find the amount money raised by Heddy.
So, we will substitute the value of the variable in the expression for the amount as 2/3(x−7.5).then, we will simplify it and get the required amount.
So, we write the expression for the amount of money raised by Heddy as follows:
⇒2/3(x−7.5)
Substitutingx=170.5 as found in the part (a), we get
⇒2/3(170.5−7.5)
⇒2/3(163)
⇒326/3
⇒108.67
So, the amount of money raised by Heddy is $108.67.
The amount of money raised by Heddy is found as $108.67.
Page 29 Problem 29 Answer
Here, we have to find the amount of money raised by Hailey.
So, we have the expression for this amount as 2(x−7.5)−4.
We will substitute the value of x as determined in part (a) of this question and simplify.
So, we write the expression for the amount of money raised by Hailey as per the question as follows:
⇒2(x−7.5)−4
Substitutingx=170.5 in the above expression, we get
⇒2(170.5−7.5)−4
⇒2(163)−4
⇒326−4
⇒322
So, the amount of money raised by Hailey is $322.
The amount of money raised by Hailey is found as $322.
Page 30 Problem 30 Answer
Here, we have to explain if Harry and Henry together have raised the same amount of money as Helen.
So, we will add the amounts added by Harry and Henry and check if the sum is equal to amount raised by Helen.
So, we found the amounts found in the previous parts as follows:
Amount of money raised by Harry= $170.5
Amount of money raised by Henry= $163
Amount of money raised by Helen= $326
Now, adding the amounts raised by Harry and Henry, we get⇒170.5+163=333.5
So, we observe that the amount of money raised by Helen is less than the amount raised by Harry and Helen together.
Hence, we conclude that harry and Henry can never raise the same amount of money as Helen.
Harry and Henry together could never have raised the same amount of money as Helen.
Page 30 Problem 31 Answer
Here, we have to find the amount of money raised by Henry.
So, we will substitute the value of the variable as found in the part (a) and substitute it in the expression representing the amount raised by Henry.
So, we have the expression representing the amount of money raised by Henry as follows:
⇒x−7.5
Substituting x=54.375 in the above expression, we get
⇒54.375−7.5
⇒46.875
So, the amount of money raised by Henry is $46.875.
The amount of money raised by Henry is found as $46.875.
Page 30 Problem 32 Answer
Here, we have to find the amount of money raised by Helen.
So, we will substitute the value of the variable as found in the part (a) and substitute it in the expression representing the amount raised by Helen.
So, we have the expression raised by Helen as follows:
⇒2(x−7.5)
Substitutingx=54.375,
we get
⇒2(54.375−7.5)
⇒2(46.875)
⇒93.75
So, the amount of money raised by Helen is $93.75.
The amount of money raised by Helen is found as $93.75.
Page 30 Problem 33 Answer
We have been given that Heddy and Hailey raised $126.
We have to find the amount of money Heddy raised.
We will find the result by substitute the value of the variable as found in part (a) and substitute it in the expression representing the amount raised by Heddy.
So, we have the expression raised by Heddy as follows:
=6(x−7.5)
Substituting x=54.375,we get
=6(54.375−7.5)
=6(46.875)
=281.25
We have found the amount of money raised by Heddy that is,$281.25.
Page 30 Problem 34 Answer
We have been given that Heddy and Hailey raised $126.We have to find the amount of money Hailey raised.
We will find the result by substitute the value of the variable as found in part (a) and substitute it in the expression representing the amount raised by Hailey.
So, we have the expression raised by Hailey as follows:
=6(x−7.5)−4
Substituting x=54.375, we get
=6(54.375−7.5)−4
=6(46.875)−4
=281.25−4
=277.25
We have found the amount of money raised by Hailey that is,$277.25.