Into Math Grade 7 Module 2 Lesson 1 Answer Key Percent Change

We included HMH Into Math Grade 7 Answer Key PDF Module 2 Lesson 1 Percent Change to make students experts in learning maths.

HMH Into Math Grade 7 Module 2 Lesson 1 Answer Key Percent Change

I Can solve multi-step problems involving percent change.

Connect to Vocabulary
Percent change is an amount of change expressed as a percent of the original amount.
Percent increase is an amount of increase expressed as a percent of the original amount.
Percent decrease is an amount of decrease expressed as a percent of the original amount.

Step It Out

1. When a quantity increases or decreases, you can use number sense and proportional reasoning to compare the amount of change to the original amount.

A. Janis earns $7.00 per hour at Pizza King. After 6 months, her hourly rate of pay increased to $7.70 per hour. What is the percent increase in her hourly rate of pay?
The original amount is $____.
The new amount is $ ____.
The amount of change is $ ____.
Write the ratio as a percent. Note that the original amount is 10 times the amount of change.

Her rate of pay increased by ___%.
Answer:
The original amount is $7.
The new amount is $ 7.70.
The amount of change is 7.7 – 7 = $0.7
Amount of change/ original amount = 0.7/7 = 0.1 = 0.1 × 100/100 = 10%

B. Pizza King decided to decrease the price of a large pizza, as shown on their sign. What is the percent decrease in the cost of a large pizza?

The original amount is $ _____.
The new amount is $ _____.
The amount of change is $ ____.

The cost decreased by ____%.
Answer:
The original amount is $ 16.
The new amount is $ 12.
The amount of change is $16 – $12 = $4.
Amount of change/ original amount = 4/16 = 1/4 = 25%

Turn and Talk How can you use number sense to write as a percent?

2. A population of cheetahs has decreased 30% over the last 18 years. If there were originally about 12,000 cheetahs, how many cheetahs are there now?
A. What is the percent decrease in the cheetah population? What was the original population?
_______________________
Answer:
A population of cheetahs has decreased 30% over the last 18 years.
12000 × (1 – 30%)
12000 × (100 – 30)
12000 × 70%

B. Find the change in the number of cheetahs. Write the percent as a decimal.
Percent decrease × Original amount = Decrease amount
____ × _______ = _____
Answer:
12000 × 70% = 8400

C. How many cheetahs are there now?
_____ – ______ = ____, so there are about ______ cheetahs now.
Answer:
12000 – 8400 = 3600
Thus there are about 3600 cheetahs now.

Turn and Talk Can you find another way to determine how many cheetahs there are now?

3. Chasidy is changing the size of the garden shown to fit more vegetables. She plans to increase the width by 25%.

A. What will the new width be?
Increase in width: 8 × ___ = __ feet
New width: 8 + ___ = ___ feet
Answer:
Increase in width: 8 × 25% = 2 feet
New width: 8 + 2 = 10 feet

B. How much greater is the new area?
Original area: 8 × 12 = ___ ft² New area: ___ × 12 = ___ ft²
The new area is ___ square feet greater.
Answer:
Original area: 8 × 12 = 96 ft² New area: 10 × 12 = 120 ft²
120 – 96 = 24
The new area is 24 square feet greater.

C. Chasidy plans to add 5 more plants. If each vegetable plant requires a minimum of 1.25 square feet, will Chasidy’s plan work for the new dimensions of her garden?
Area needed for new plants: ____ × _____ = ft²
Will Chasidy’s plan. work? Why or why not?
_______________________
_______________________
Answer:
5 × 1.25 = 6.25 sq. ft
96 + 6.25 = 102.25 sq. feet
So. Chasidy’s plan will work.

4. A machine cuts lumber into 8-foot planks. Company regulations allow the lengths to vary by \(\frac{1}{2}\)%, which can be either an increase or decrease of \(\frac{1}{2}\)% of the intended length. Find the range of values allowed by the company’s regulations.

A. How do you express \(\frac{1}{2}\)% as a decimal?
____ ÷ 100 = ____
Answer:
\(\frac{1}{2}\) ÷ 100 = 0.005

B. What is the length, in feet, that the planks are allowed to vary? Remember, the • indicates multiplication.
____ • ____ = ____ foot
Answer: 0.005 × 8 = 0.04

C. What is the length of the shortest allowable plank and the longest allowable plank cut by the machine?
Shortest: 8 – ____ = ____ feet
Longest: 8 + ____ = ____ feet
Answer:
Shortest: 8 – 0.04 = 7.96 feet
Longest: 8 + 0.04 = 8.04 feet

Check Understanding

Question 1.
Peggy earned $20 for each lawn she mowed last summer. This summer, she raised her price to $23 per lawn. What is the percent increase of Peggy’s charges?
Answer:
Given,
Peggy earned $20 for each lawn she mowed last summer.
This summer, she raised her price to $23 per lawn.
(23 – 20) ÷ 20 = 3/20
Multiply and divide by 5
3/20 × 5/5 = 15/100 = 15%
The percent increase is 15%.

Question 2.
Robert is inspecting a shipment of 22-inch pipes. The lengths of the pipes may vary by 1 %. What is the range of allowable lengths of the pipes?
Answer:
Given,
Robert is inspecting a shipment of 22-inch pipes.
The lengths of the pipes may vary by 1 %.
22 × 1% = 22 × 0.01 = 0.22 inch
22 + 0.22 = 22.22 inch
22 – 0.22 = 21.78 inch
Thus the range of allowable lengths of the pipes is [21.78, 22.22]

Question 3.
When Bart bought his car, it averaged 28 miles per gallon of gas. Now, the car’s average miles per gallon has decreased by 14%. What is the car’s average miles per gallon now? Round your answer to the nearest mile per gallon.
Answer:
Given,
When Bart bought his car, it averaged 28 miles per gallon of gas.
Now, the car’s average miles per gallon has decreased by 14%.
28 × 14% = 3.92
28 – 3.92 = 24.08 ≈ 24 miles/gallon of gas
Therefore the answer is 24 miles per gallon of gas.

Question 4.
A number changes from 50 to 76. What type of percent change is this? Calculate the percent change.
Answer:
(50 – 76) ÷ 50
-26/50
Multiply and divide by 2.
-26/50 × 2/2 = -52/100 = -52%
The percent decrease is 52%

Question 5.
The data plan for Shawn’s phone has 32,000 megabytes of storage for photos. She wants to increase the amount of data by 4%. If each photo uses 5 megabytes, will she have enough new memory for 200 additional photos? Explain.
Answer:
Given,
The data plan for Shawn’s phone has 32,000 megabytes of storage for photos.
She wants to increase the amount of data by 4%.
32000 × (1 + 4%)
32000 × (1 + 0.04)
32000 × 1.04 = 33280

On Your Own

Question 6.
The population of deer in a protected area is 225. If the population increases at a rate of 24% per year, how many deer will be in the area next year?

Answer:
Given,
The population of deer in a protected area is 225.
Rate = 24%
225 × (1 + 24%)
225 × (1 + 0.24)
225 × 1.24 = 279
There will be 279 deers in the area next year.

Question 7.
There are 75 students enrolled in a camp. The day before the camp begins, 8% of the students cancel. How many students actually attend the camp?
Answer:
There are 75 students enrolled in a camp.
The day before the camp begins, 8% of the students cancel.
75 × 8% = 6
75 – 6 = 69
Thus 69 students actually attend the camp.

Question 8.
Two years ago, a car was valued at $24,000. This year, the value of the car is $23,160. What was the percent decrease in the value of the car?
Answer:
Given,
Two years ago, a car was valued at $24,000.
This year, the value of the car is $23,160.
(24000 – 23160) ÷ 24000 = 7/200 = 0.035
Multiply and divide by 100
0.035 × 100/100 = 3.5%
The percent decrease in the value of the car is 3.5%

Question 9.
Mr. Milton had $1,200 in his savings account at the beginning of the year. If his account has a balance of $1,230 at the end of the year, what is the percent increase of his balance?
Answer:
Given,
Mr. Milton had $1,200 in his savings account at the beginning of the year.
If his account has a balance of $1,230 at the end of the year.
(1230 – 1200) ÷ 1200 = 30/1200 = 1/40 = 0.025
Multiply and divide by 100
0.025 × 100/100 = 2.5/100 = 2.5%
The percent increase of his balance is 2.5%

Question 10.
Last year, 140 people in a community had cell phones. This year, the number of people in the community with cell phones has increased by 65%.

A. What is the percent of increase?
_______________________
Answer:
This year, the number of people in the community with cell phones has increased by 65%.
So, the percent of increase is 65%.

B. What is the change in the number of people with cell phones?
_______________________
Answer:
140 × (1 + 65%)
140 × (1 + 0.65)
140 × 1.65 = 231

C. How many people in the community have cell phones this year?
_______________________
Answer: Thus 231 people in the community have cell phones this year.

Question 11.
A library has 300 feet of shelves for books. The library will increase the number of feet of shelves by 18%.

A. How many feet of shelves are being added?
_______________________
Answer:
Given,
A library has 300 feet of shelves for books.
The library will increase the number of feet of shelves by 18%.
300 × 18%
300 × 18/100 = 54 feet

B. How many feet of shelves will the library have after the new shelves are installed?
_______________________
Answer:
300(1 + 18%)
300 × 1.18 = 354 feet

C. The library plans to add 1,000 books to its collection. If the library can fit 15 books on each foot of shelving, will the library have enough room on the new shelves for all the new books? Explain.
_______________________
Answer:
The library plans to add 1,000 books to its collection.
354 × 15 = 5310 books
54 × 15 = 810 books
810 is less than 1000 books
Thus the library cannot have enough room on the new shelves for all the new books.

Question 12.
A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. The village plans to increase the length by 30%.

A. What will be the new length of the parking lot?
_______________________
Answer:
Given,
A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars.
The village plans to increase the length by 30%.
180 × (1 + 30%)
180 × (1 + 30/100)
180 × (1 + 0.3)
180 × 1.3 = 234 feet

B. How much greater is the new area?
_______________________
Answer:
Increased area: 180 × 30% × 120 = 6480 sq. feet

C. Construct Arguments If each car needs about 288 square feet in a parking lot, will the new parking lot be able to fit 20 more cars than the original parking lot? Explain.
_______________________
Answer:
6480 ÷ 288 = 22.5 > 20
So, the new parking lot is able to fit 20 more cars than the original parking lot.

For Problems 13-20, find each percent change. State whether it is an increase or decrease.

Question 13.
From 50 to 22
_______________________
Answer:
(50 – 22)÷ 50
28/50
Convert into percent change by multiplying and dividing by 2.
28/50 × 2/2 = 56/100 = 56%
Percent change increases.

Question 14.
From 50 to 43
_______________________
Answer:
(50 – 43) ÷ 50
7/50
Convert into percent change by multiplying and dividing by 2.
7/50 × 2/2 = 14/100 = 14%
Percent change increases.

Question 15.
From 20 to 35
_______________________
Answer:
(20 – 35) ÷ 20
-15/20
Convert into percent change by multiplying and dividing by 5.
-15/20 × 5/5 = -75/100 = -75%
Percent change decreases.

Question 16.
From 112 to 140
_______________________
Answer:
(112 – 140) ÷ 112
-28/112 = -1/4
Convert into percent change by multiplying and dividing by 25.
-1/4 × 25/25 = -25/100 = -25%
Percent change decreases.

Question 17.
From 40 to 38
_______________________
Answer:
(40 – 38) ÷ 40
2/40 = 1/20
Convert into percent change by multiplying and dividing by 5
1/20 × 5/5 = 5/100 = 5%
Percent change increases.

Question 18.
From 60 to 36
_______________________
Answer:
(60 – 36) ÷ 60
24/60 = 2/5
Convert into percent change by multiplying and dividing by 20.
2/5 × 20/20 = 40/100 = 40%
Percent change increases.

Question 19.
From 28 to 42
_______________________
Answer:
(28 – 42) ÷ 28
-14/28 = -2/4
Convert into percent change by multiplying and dividing by 25.
-2/4 × 25/25 = -50/100 = -50%
Percent change decreases.

Question 20.
From 80 to 128
_______________________
Answer:
(80 – 128) ÷ 80
-48/120 = -4/10 = -2/5
Convert into percent change by multiplying and dividing by 20.
-2/5 × 20/20 = -40/100 = -40%
Percent change decreases.

Question 21.
A display for rolls of tape indicates that each roll contains 150 yards of tape. If the actual length of tape can vary by 2.5% of that amount, what is the range for the length of tape on a roll? f

Answer:
Given,
A display for rolls of tape indicates that each roll contains 150 yards of tape.
The actual length of tape can vary by 2.5% of that amount.
150 × (1 + 2.5%) = 153.75
150 × (1 – 2.5%) = 146.25
The range is [146.25, 153.75]

Question 22.
An airline states that an airplane flight between two cities takes 2.5 hours. The airline also says that the actual flying time can change by up to 15% of that amount. What are the shortest and longest times for the airplane flight? Round your answers to the nearest tenth of an hour.
_______________________
Answer:
Given,
An airline states that an airplane flight between two cities takes 2.5 hours.
The airline also says that the actual flying time can change by up to 15% of that amount.
The shortest: 2.5 × (1 – 15%) = 2.1 hours
The longest: 2.5 × (1 + 15%) = 2.9 hours

For Problems 23-28, find the range of allowable values based on the given information. Round to the nearest tenth.

Question 23.
15; can vary by 2%
_______________________
Answer:
2% of 15
2/100 × 15
0.02 × 15 = 0.3
Upper limit: 15 + 0.3 = 15.3
Lower Limit: 15 – 0.3 = 14.7
Hence the range is 14.7 to 15.3

Question 24.
24; can vary by 3.5%
_______________________
Answer:
3.5% of 24
3.5/100 × 24 = 0.84
Upper limit: 24 + 0.84 = 24.84
Lower limit: 24 – 0.84 = 23.16
Hence the range is 23.16 to 24.84

Question 25.
31; can vary by 7%
_______________________
Answer:
7% of 31
7/100 × 31 = 2.17 = 2.2
Upper limit: 31 + 2.2 = 33.2
Lower limit: 31 – 2.2 = 28.8
Hence the range is 28.8 to 33.2

Question 26.
44; can vary by 4.2%
_______________________
Answer:
4.2% of 44
4.2/100 × 44 = 1.848 = 1.9
Upper limit: 44 + 1.9 = 45.9
Lower limit: 44 – 1.9 = 42.1
Hence the range is 42.1 to 45.9

Question 27.
49; can vary by 8.1%
_______________________
Answer:
8.1% of 49
8.1/100 × 49 = 3.96 = 4
Upper limit: 49 + 4 = 53
Lower limit: 49 – 4 = 45
Hence the range is 45 to 53.

Question 28.
50; can vary by 30%
_______________________
Answer:
30% of 50
30/100 × 50 = 15
Upper limit: 50 + 15 = 65
Lower limit: 50 – 15 = 35
Hence the range is 35 to 65.

Question 29.
Last year, one model of a gasoline-powered car had a gas tank that holds 22 gallons of gas. This year, the carmaker is going to increase the capacity of the gas tank by 15%. The car’s mileage both last year and this year, is 23 miles per gallon. Will this year’s model be able to travel 100 miles farther on a single tank of gas? Explain.
Answer:
Given,
Last year, one model of a gasoline-powered car had a gas tank that holds 22 gallons of gas.
This year, the carmaker is going to increase the capacity of the gas tank by 15%.
The car’s mileage both last year and this year, is 23 miles per gallon.
22 × 23 = 506 miles
This year the gas tank can hold
22 × (1 + 15%)
22 × 1.15 = 25.3 gallons of gas
25.3 × 23 = 581.9 miles
581.9 – 5.6 = 75.9 < 100 miles.
Hence this year’s model will not be able to travel 100 miles farther on a single of gas.

Question 30.
During a job fair last year, an employer spent 200 minutes interviewing people for jobs. This year, the employer wants to interview at least 4 more people than last year. The company will increase the amount of interviewing time by 40%. If each interview, both last year and this year, takes about 15 minutes, will the employer meet its goal? Explain.
Answer:
Given,
During a job fair last year, an employer spent 200 minutes interviewing people for jobs.
This year, the employer wants to interview at least 4 more people than last year.
The company will increase the amount of interviewing time by 40%.
Last year: 200 ÷ 15 ≅ 13
This year: 200 × (1 + 40%) ÷ 15 ≈ 18
18 – 13 = 5 >4
Therefore the employer meet its goal.

Question 31.
Martin is building a rectangular fire pit in his backyard. He dug a hole 30 inches by 30 inches. He decides to make each side of the pit 6 inches longer. What is the percent increase in the area of the fire pit?
Answer:
Given,
Martin is building a rectangular fire pit in his backyard.
He dug a hole 30 inches by 30 inches.
He decides to make each side of the pit 6 inches longer.
P = (36 × 36 – 30 × 30)/(30 × 30) × 100% = 44%

Question 32.
Attend to Precision A peanut butter company is changing its packaging. The current container holds 16 ounces of peanut butter. The new container will hold 14 ounces. What is the percent decrease in volume for the new package? Round your answer to the nearest tenth.
Answer:
Given,
A peanut butter company is changing its packaging.
The current container holds 16 ounces of peanut butter.
The new container will hold 14 ounces.
(14 – 16) ÷ 14
-2/14 = -1/7
-1/7 = 0.14
-0.14 × 100/100 = -14%
The percent decrease in volume for the new package is 14%

Lesson 2.1 More Practice/Homework

Percent Change

Question 1.
Five years ago, an average model 70” TV cost about $2,400. Now a similar TV costs approximately $1,680. What is the percent decrease in TV price?
Answer:
Given,
Five years ago, an average model 70” TV cost about $2,400.
Now a similar TV costs approximately $1,680.
(2400 – 1680) ÷ 2400
720/2400 = 3/10
3/10 × 10/10 = 30/100 = 30%
Thus the percent decrease in TV price is 30%

Question 2.
Antoine made $33,284 last year. He received a 4.5% annual raise. What will his new salary be for the coming year?
Answer:
Given,
Antoine made $33,284 last year.
He received a 4.5% annual raise.
33284 × (1 + 4.5%)
33284 × (1 + 4.5/100)
33284 × (1 + 0.045)
33284 × 1.045 = 34781.75
Antoine salary will be $34781.75 for the coming year.

Question 3.
STEM A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased as shown. How many bacteria are there now?

Answer:
Given,
A scientist observes and counts 155 bacteria in a culture.
The number of bacteria has increased by 40%.
155 × (1 + 40%)
155 × (1 + 0.4)
155 × 1.4 = 217

Question 4.
The number of veggie burgers sold at a restaurant in Houston, Texas, was 425 in April. The number sold in May was 16% less than the number sold in April. How many veggie burgers were sold in May?
Answer:
Given,
The number of veggie burgers sold at a restaurant in Houston, Texas, was 425 in April.
The number sold in May was 16% less than the number sold in April.
425 × (1 – 16%)
425 × (1 – 0.16)
425 × 0.84 = 357
Therefore 357 burgers were sold in May.

Question 5.
A warehouse worker fills 150 orders per day on average. From day to day, the number of orders varies by 2%. What is the range of the number of orders the worker fills each day?
Answer:
Given,
A warehouse worker fills 150 orders per day on average.
From day to day, the number of orders varies by 2%.
150 × 2% = 150 × 0.02 = 3
150 – 3 = 147
150 + 3 = 153
A change of 2% per day is 3 orders per day, so it could go up by 3 or it could go down by 3.
The range is 147 to 153.

Question 6.
Find the percent change from 96 to 93. State whether it is an increase or decrease.
Answer:
(96 – 93)/96 = 3/96 = 1/32
Convert the fraction to the decimal form.
1/32 = 0.031
Multiply and divide by 100 to convert into percent
0.03125 × 100/100 = 3.125/100
= 3.125%
The Answer is Increase.

Question 7.
Find the percent change from 32 to 60. State whether it is an increase or decrease.
Answer:
(32 – 60)/60
= -28/32
= -7/8
Convert the fraction to the decimal form.
-7/8 = -0.875
Multiply and divide by 100 to convert into percent
-0.875 × 100/100
= -87.5/100
= -87.5%
The answer is decrease.

Question 8.
Find the range of allowable values based on a measure of 130 inches if the values can vary by 1.4%.
Answer:
130 × 1.4%
130 × 1.4/100
130 × 0.014 = 1.82
130 – 1.82 ≤ x ≤ 130 + 1.82
128.18 ≤ x ≤ 131.82
Thus the range is [128.18, 131.82]

Question 9.
Attend to Precision In Cary’s basketball career, he’s made 80% of his free throws, plus or minus 5%. If he attempts 200 free throws this season, what is the range of successful free throws he can expect to make? Show your calculation.
Answer:
Given,
200 × 5%
= 200 × 5/100 = 10
200 + 10 = 210
200 – 10 = 190
Therefore the range of successful free throws he can expect to make is 190 ∼ 210.

Test Prep

Question 10.
A collector bought a rare coin for $30. The coin is now valued at $37.50. Select all the true statements.
A. The scenario represents a percent increase.
B. The scenario represents a percent decrease.
C. The percent of change was 20%.
D. The percent of change was 25%.
E. The percent of change was 75%.
Answer:
Given,
A collector bought a rare coin for $30. The coin is now valued at $37.50.
37.50 > 30
So, statement A is true and B is false.
(37.5 – 30) ÷ 30 × 100%
= 7.5 ÷ 30 × 100% = 25%
So, Statement D is true.
Thus option A and D are the correct answers.

Question 11.
A coffee machine dispenses 8-ounce cups of coffee automatically. The amount of coffee may vary by 3%. What are the least and greatest number of ounces the coffee machine may dispense?
Least number: ___ ounces Greatest number: ____ ounces
Answer:
Given,
A coffee machine dispenses 8-ounce cups of coffee automatically.
The amount of coffee may vary by 3%.
8 × (1 – 3%)
8 × (100%- 3%)
8 × 97%
8 × 0.97 = 7.76 ounces
8 × (1 + 3%)
8 × (100% + 3%)
8 × 103%
8 × 1.03 = 8.24 ounces
The coffee machine may dispense the least 7.76 ounces and the greatest 8.24 ounces.

Question 12.
A German shepherd puppy weighed 25 pounds at 4 months old and 31 pounds at 5 months old. What is the percent increase or decrease of its weight?
A. 24% increase
B. 35% decrease
C. 35% increase
D. 54% decrease
Answer:
Given,
A German shepherd puppy weighed 25 pounds at 4 months old and 31 pounds at 5 months old.
31 > 25
The percent increase of its weight.
(31 – 25)/25 × 100% = 24%
Thus option A is the correct answer.

Question 13.
The butterfly population at Glen Arbor Farms was 250 last year. This year there are 100 butterflies. What is the percent increase or decrease?
A. 50% decrease
B. 50% increase
C. 60% decrease
D. 60% increase
Answer:
Given,
The butterfly population at Glen Arbor Farms was 250 last year.
This year there are 100 butterflies.
(100 – 250) ÷ 250
-150/250
= -3/5
Convert it into a percent by multiplying and dividing by 20.
-3/5 × 20/20 = -60/100 = -60%
60% decrease
Thus option C is the correct answer.

Spiral Review

Question 14.
There is a proportional relationship between time in hours and time in days.
A. What is the constant of proportionality?
_______________________
Answer:
We know that,
1 day = 24 hours
y = 24x
y/x = 24
So, the constant of proportionality is 24.

B. What equation describes this relationship?
_______________________
Answer:
The equation is y = 24x
y represents the time in days
x represents the time in hours

Question 15.
A triangle has a base length of 10 inches and a height of 4 inches. What is the area of the triangle?
_______________________
Answer:
Given,
A triangle has a base length of 10 inches and a height of 4 inches
We know that,
Area of the triangle = 1/2 ×  b × h
A = 1/2 × 10 × 4
A = 20 sq. inches
Thus the area of the triangle is 20 sq. inches.