Glencoe Math Course 2 Volume 1 Common Core Chapter 2 Percents
Page 103 Exercise 1 Problem 1
We need to explain how can percent help you understand situations involving money.
The percent help to understand situations involving money
The interest rates are written as a percent.
Also, find the interest earned on a savings account and the amount of interest charged on bank loans and credit cards.
The sales tax is also indicated in percent.
Hence explained.
Page 103 Exercise 2 Problem 2
Given:
To show that the 60% of 2000 = 1200
To prove that the 60% of 2000 = 1200
\(\frac{60}{100}\) (2000) = 1200
60 × 20 = 1200
1200 = 1200
Thus the 60% of 2000 = 1200 is proved
Page 106 Exercise 1 Problem 3
Given:
To find – The number from 8% of 50
8% of 50
\(\frac{8}{100}\)(50)
= 4
8% of 50 is 4
8% of 50 is 4
Page 106 Exercise 2 Problem 4
Given:
Find each number. Round to the nearest tenth if necessary.
To find – The number of 95 % of 40
Given:
95 % of 40
95 % = \(\frac{95}{100}\)
Then \(\frac{95}{100}\) of 40
= \(\frac{95}{100}\) × 40
⇒ \(\frac{95}{5}\) × 2
⇒ 19 × 2 = 38
So, 95 % of 40 is 38.
The solution is 38.
Page 106 Exercise 3 Problem 5
Given:
Find each number. Round to the nearest tenth if necessary.
To find – The number of 110 % of 70
Given:
110 % of 70
110 % = \(\frac{110}{100}\)
Then \(\frac{110}{100}\) of 70
= \(\frac{110}{100}\) × 70
⇒ 11 × 7= 77
So, 110 % of 70 is 77.
The solution is 77.
Page 106 Exercise 4 Problem 6
Given:
Mackenzie wants to buy a backpack that costs $50.If the tax rate is 6.5%, how much tax will she pay?
To find – The amount of tax.
Cost of backpack = $50
Tax rate = 6.5%
Amount of tax = 6.5 % of 50
6.5 % = \(\frac{6.5}{100}\)
Then \(\frac{6.5}{100}\) of 50
= \(\frac{6.5}{100}\) × 50
⇒ \(\frac{6.5}{2}\)
= 3.25
So the amount of tax = $3.25
The solution is $3.25
Page 106 Exercise 5 Problem 7
Given:
Building on the essential question give an example of a real-world situation in which you would find the percent of a number.
To find – An example.
Take an example of 17% of 150 oranges are bad.
To find the number of oranges are bad.
17 % of 150
17 % = \(\frac{17}{100}\)
\(\frac{17}{100}\) of 150
= \(\frac{17}{100}\) × 150
⇒ \(\frac{17}{2}\) × 3 = 26
So, 26 oranges are bad.
Hence the example has been found.
Page 107 Exercise 2 Problem 8
Given:
Find each number. Round to the nearest tenth if necessary.
45% of $432
To find – The number.
Given:
45 % of 432
45 % \(\frac{45}{100}\)
Then,\(\frac{45}{100}\) of 432
= \(\frac{45}{100}\) × 432
& ⇒ \(\frac{9}{5}\) × 108 = 194.4
So,45% of $432 is $194.4
The solution is 194.4
Page 107 Exercise 3 Problem 9
Given:
Find each number. Round to the nearest tenth if necessary.
3.23% of $640
To find –The number.
Given:
23 % of 640
23 % = \(\frac{23}{100}\)
Then \(\frac{23}{100}\) of 640
= \(\frac{23}{100}\) × 640
= \(\frac{23}{5}\) × 32
= 147.2
So, 23 % of $640 is $147.2
The solution is 147.2
Page 107 Exercise 4 Problem 10
Given:
Find each number. Round to the nearest tenth if necessary.
4.130% of 20
To find – The number.
Given:
130 % of 20
130 % = \(\frac{130}{100}\)
Then \(\frac{130}{100}\) of 20
= \(\frac{130}{100}\) × 20
⇒ 13 × 2 = 26
So,130 % of 20 is 26
The solution is 26
Page 107 Exercise 7 Problem 11
Given:
Find each number. Round to the nearest tenth if necessary.
7.32% of 4
To find – The number.
Given:
32 %of 4
32 = \(\frac{32}{100}\)
Then, \(\frac{32}{100}\) of 4
= \(\frac{32}{100}\) × 4
⇒ \(\frac{32}{25}\)
= 1.28
So, 32 % of 4 is 1.28.
The solution is 1.28
Page 107 Exercise 9 Problem 12
Given:
Find each number. Round to the nearest tenth if necessary.
9.23.5%of 128
To find – The number.
Given:
⇒ 23.5
Then, \(\frac{23.5}{100}\) of 128
= \(\frac{23.5}{100}\) × 128
=\(\frac{23.5}{25}\) × 32
= 30.08
So,23.5 % of 128 is 30.08
The solution is 30.08
Page 107 Exercise 10 Problem 13
Given:
Suppose there are 20 questions on a multiple-choice test.
If 25% of the answers are choice B, how many of the answers are not choice B?
To find the number of answers are not choice B.
Total number of questions = 20
25% of the answers are choice B
Therefore, the number of answers are choice B = 25% of 20
\(\frac{32}{100}\)of 20 = \(\frac{32}{100}\) × 20
⇒ \(\frac{1}{4}\) × 20
= 5
The number of answers are choice B = 5
So, the number of answers are not choice B = 20 − 5
= 15
The number of answers are not choice B = 15
Page 107 Exercise 11 Problem 14
Given:
To find – The dollar amount of the group discount each student would receive at each park.
At pirate bay 20% discount of $35.95
\(\frac{20}{100}\) of 35.95 = \(\frac{20}{100}\) ×35.95
⇒ \(\frac{1}{5}\) × 35.95
= 7.19
At funtopia 15% discount of $29.75
\(\frac{15}{100}\)of 29.75 = \(\frac{15}{100}\) ×29.75
⇒ \(\frac{3}{20}\) × 29.75 = 4.46
At zoomland 25% discount of $38.49
\(\frac{25}{100}\) of 38.49 = \(\frac{25}{100}\) × 38.49
⇒ \(\frac{1}{4}\) × 38.49
= 9.62
$7.19 at pirate bay,$4.46 at funtopia, and $9.62 at zoomland.
The dollar amount of the group discount each student would receive is $7.19 at pirate bay,$4.46 at funtopia, and $9.62 at zoomland.
Page 108 Exercise 14 Problem 15
Given:
Find each number. Round to the nearest hundredth.
5\(\frac{1}{2}\)% of 60
To find – The number.
Given:
5\(\frac{1}{2}\)% of 60
5\(\frac{1}{4}\) = \(\frac{11}{2}\)%
= \(\frac{11/2}{100}\)
= \(\frac{11}{200}\)
5\(\frac{1}{2}\)% of 60 = \(\frac{11}{200}\)× 60
\(\frac{11}{10}\) × 3 = 3.3
So 5\(\frac{1}{2}\)% of 60 is 3.3.
The solution is 3.3
Page 108 Exercise 15 Problem 16
Given:
Find each number. Round to the nearest hundredth.
20\(\frac{1}{4}\)% of 3
To find – The number.
Given:
20\(\frac{1}{4}\)% of 3
20\(\frac{1}{4}\) = \(\frac{81}{4}\)%
\(\frac{81/4}{100}\) = \(\frac{81}{400}\)
20\(\frac{1}{4}\)% of 3 = \(\frac{81}{400}\) × 3
⇒ 0.6075 ≃ 0.608
So , 20\(\frac{1}{4}\)% of 3 is 0.608
The solution is 0.608
Page 108 Exercise 16 Problem 17
Given:
Find each number. Round to the nearest hundredth.
1,000 % of 99
To find – The number.
Given:
1,000 % of 99
1000 % \(\frac{1000}{100}\) = 10
1,000 % of 99 = 10 × 99
⇒ 990
So, 1,000 % of 99 is 990
The solution is 990
Page 108 Exercise 17 Problem 18
Given:
To convert a percentage to a number 520% of 100
520% of 100
\(\frac{520}{100}\)(100)
= 520
520% of 100 = 520
The answer is 520
Page 108 Exercise 19 Problem 19
Given:
To convert a percentage to a number 200% of 79
200% of 79
\(\frac{200}{100}\)(79)
= 2(79)
= 158
200% of 79 = 158
The answer 200% of 79 is 158
Page 108 Exercise 21 Problem 20
Given:
To convert a percentage to a number 0.28% of 50
0.28% of 50
\(\frac{0.28}{100}\)(50)
= \(\frac{0.28}{10}\)(5)
= \(\frac{0.25}{2}\)
= 0.14
0.28% of 50 = 0.14
The answer 0.28% of 50 is 0.14
Page 108 Exercise 23 Problem 21
Given:
To explain the percentage has been done easier with fractions or decimal
Solution :
Its easier to use a decimal
Percent means a part of 100 x /100 = x%
If you have a decimal, just move the decimal place to the left of 2 places
If you have a fraction, try to get the denominator equal to 100, or divide it out and move the
A decimal place to the left 2 places
Decimal is easier than a fraction
The answer 0 is a decimal is easier than a fraction
Page 108 Exercise 24 Problem 22
Given:
To choose the correct option in how much he left to spend
Solution :
Option c is correct
(1) He will spend 18% of the repair
\(\frac{18}{100}\)(300)
= (18)(3)
= 54
He spends $54 on repair
(2) 20% of savings
\(\frac{20}{100}\) (300)
= 60
(C) 35% of the canvas
\(\frac{35}{100}\)(300)
= 105
He will spend $54 on repair and $60in savings and $105 in canvas and leaving him $81
The answer $81 option c is correct
Page 109 Exercise 25 Problem 23
Given:
To convert the percentage into number 54% of 85
Solution :
54% of 85
\(\frac{54}{100}\)(85)
= 54(0.85)
= 45.9
54% of 85 = 45.9
The answer for 54% of 85 is 45.9
Page 109 Exercise 26 Problem 24
Given:
To convert the percentage into number 12% of $230
Solution:
12% of $230
\(\frac{12}{100}\)(230)
= 0.12(230)
= 27.6
12% of $230 = 27.6
The answer for 12% of $230 is $27.6
Page 109 Exercise 27 Problem 25
Given:
To convert the percentage into number 98% of 15
Solution :
98% of 15
\(\frac{98}{100}\)(15)
= 0.98(15)
= 14.7
98% of 15 = 14.7
The answer for 98% of 15 = 14.7
Page 109 Exercise 28 Problem 26
Given:
To convert the percentage into number 250% of 25
Solution :
250% of 25
\(\frac{250}{100}\)(25)
= 2.5(25)
= 62.5
250% of 25 = 62.5
The answer for 250% of 25 is 62.5
Page 109 Exercise 31 Problem 27
Given:
To convert the percentage into number 0.5% of 60
Solution :
0.5% of 60
\(\frac{0.5}{100}\)(60)
= \(\frac{0.5}{10}\) (6)
= 0.3
0.5% of 60 = 0.3
The answer for 0.5% of 60 is 0.3
Page 109 Exercise 32 Problem 28
Given:
To convert the percentage into number 2.4% of 20
Solution :
2.4% of 20
\(\frac{2.4}{100}\)(20)
= \(\frac{2.4}{10}\)(2)
= 0.48
2.4% of 20 = 0.48
The answer for 2.4% of 20 = 0.48
Page 109 Exercise 34 Problem 29
Given:
To find – How many households watched the finals
Solution :
17.7% of 110.2
Turn percent to decimals
\(\frac{17.7}{100}\)(110.2)
= 0.177(110.2)
= 19.51
17.7% of 110.2 = 19.51
19.51 million households watched the finals
The answer is 19.51 million households watched the finals
Page 109 Exercise 35 Problem 30
Given:
To find – What will be the cost for internet access after the increase
Solution :
The amount family paid = $19
The cost will increase by 5%
5% of 19
\(\frac{5}{100}\)(19)
= 0.05(19)
= 19.95
5% of 19 = 19.95
The cost would be $19.95
The answer is the cost would be $19.95
Page 110 Exercise 38 Problem 31
Given:
To choose the answer for how many costumers prefer horror movies
Solution :
Total no of costumer 200
The percentage of customers who prefers horror movies is 46%
46% of 200
\(\frac{46}{100}\)(200)
= 0.46(200)
= 92
46% of 200 = 92
92 customer prefer horror movies
The answer is 92 customer prefer horror movies is correct
Page 110 Exercise 39 Problem 32
Given:
The bar graph shows Ramirez’s family budget.
Ramirez monthly income is 3000 dollars.
To find:
By satisfying the following condition and finding which statement is true.
Solution :
The monthly income of Ramirez is $3000
1. The family budget is $ 1000 for rent.
To find – It in percent
\(\frac{1000}{3000}\) × 100
= 33.33
But the bar diagram shows 50% has been spent for rent so it is not correct.
2. The family budget is $ 600 for food.
\(\frac{600}{3000}\) × 100
= 20
The diagram shows 20% for their food Hence it is true
3. The family budget is $100 more for utilities than for other
\(\frac{100}{3000}\) × 100
= 3.33
But the diagram shows more than 10 for this, Hence this is false.
4. The family budget is $900 more for food than for rent.
\(\frac{900}{3000}\)×100
= 90
The bar diagram shows 10-20 % for this, hence it is false.
Answer : All of this option (2) is 20% for their food is true.
By checking all the conditions with the bar graph, The answer option g, 20% for their food is true.
Page 110 Exercise 40 Problem 33
Given:
To multiply the given number
Solution :
Multiply With digits
1.7 × 54 = 91.8
The answer is 91.8
Page 110 Exercise 41 Problem 34
Given:
Multiply:
41.1.5 × 3.65
To multiply.
Multiplying
1.5 × 3.65
= 5.475
The solution is 5.475
Page 110 Exercise 42 Problem 35
Given:
Multiply:
42. 49.6×2.7
To multiply.
Multiplying
49.6 × 2.7
= 133.92
The solution is 133.92
Page 110 Exercise 43 Problem 36
Given:
43 .trent spent 50 minutes at the neighbor’s house.
He spent 2/5 of the time swimming.
How many minutes did trent spend swimming?
To find the time trent spends swimming.
Total time trent spent in neighbor’s house = 50 minutes
Time he spent in swimming = \(\frac{2}{5}\) of 50 minutes
⇒ \(\frac{2}{5}\) × 50 = 20
The time trent spent in swimming = 20 minutes.
The time trent spent in swimming = 20 minutes.
Page 110 Exercise 44 Problem 37
Given:
There are 240 seventh-graders at Yorktown middle school.
Two-thirds of the students participate in after-school activities.
To find – The number of students who participate in after-school activities.
Number of seventh-graders at Yorktown middle school = 240
Students participate in after-school activities = \(\frac{2}{3}\) of 240
⇒ \(\frac{2}{3}\) × 240 = 160
The number of students participated in after-school activities = 160
The number of students participated in after-school activities = 160