(7) Lesson 2.5

1. Course 2, Lesson 2-5
Use the determine reasonable answers strategy to solve Exercises 1–4.
1. If the speed limit is 65 miles per hour, what is a reasonable amount of time
for the Blackwells to travel 300 miles?
2. There are 400 boys at Oak Middle School and 12% play football. What is a
reasonable number of boys that play football?
3. Suppose you are going to dinner and a movie with a friend. If you spend
$18 and the movie is 62% of the cost, what is a reasonable cost for dinner?
4. Lisa has 6 coins that total $0.86. What are the coins?
5. A number is multiplied by 13. Then 5 is subtracted from the product. The
result is 60. What is the number?

2. Course 2, Lesson 2-5
ANSWERS
1. 5 hours
2. 50
3. $7.00
4. 3 quarters, 2 nickels, 1 penny
5. 5

3. HOW can percent help you understand
situations involving money?
Ratios and Proportional Relationships
Course 2, Lesson 2-5

4. Ratios and Proportional Relationships
Course 2, Lesson 2-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
• 7.RP.3
Use proportional relationships to solve multistep ratio and percent
problems.
• 7.EE.3
Solve multistep real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. Apply
properties of operations to calculate with numbers in any form;
convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and
estimation strategies.

5. Ratios and Proportional Relationships
Course 2, Lesson 2-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.

6. • Find percent of change
• Find percent error
Ratios and Proportional Relationships
Course 2, Lesson 2-5

7. Ratios and Proportional Relationships
Course 2, Lesson 2-5
• percent of change
• percent of increase
• percent of decrease
• percent error

8. Ratios and Proportional Relationships
Course 2, Lesson 2-5
Words A percent of change is a ratio that compares the change in
quantity to the original amount.
Equation percent of change = amount of change
original amount

9. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Find the percent of change in the cost of
gasoline from 1970 to 2010. Round to the
nearest whole percent if necessary.
Since the 2010 price is greater than the 1970
price, this is a percent of increase.
Find the amount of increase.
Find the percent of increase.
percent of increase =
= Substitution
Simplify.
Write 1.27 as a percent.
≈
≈
1.27
127%
The cost of gasoline increased by about 127% from 1970 to 2010.
$2.95 – $1.30 = $1.65

10. Answer
Need Another Example?
Jonas has been saving for a video game. Last
year it cost $28. This year it costs $36. Find the
percent of change in the cost. Round to the
nearest whole percent if necessary.
29%

11. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Yusuf bought a DVD recorder for $280. Now, it is on sale for $220. Find the
percent of change in the price. Round to the nearest whole percent if necessary.
Since the new price is less than the original price, this is a percent of decrease.
Find the amount of decrease.
Find the percent of decrease.
percent of decrease =
=
≈
≈
0.21
21%
Substitution
Simplify.
Write 0.21 as a percent.
The price of the DVD recorder decreased by about 21%.
$280 – $220 = $60

12. Answer
Need Another Example?
Last month 349 books were checked out from
the school library. This month, 273 books were
checked out. Find the percent of change in the
number checked out. Round to the nearest
whole percent if necessary.
22%

13. Ratios and Proportional Relationships
Course 2, Lesson 2-5
Words The is a ratio that compares the inaccuracy
of an estimate, or amount of error, to the actual amount.
Equation percent error = amount of error
actual amount
percent error

14. 1
Need Another Example?
2
3
Step-by-Step Example
3. Ahmed wants to practice free-throws. He estimates the distance from the
free-throw line to the hoop and marks it with chalk. Ahmed’s estimate was
13.5 feet. The actual distance should be 15 feet. Find the percent error.
Find the amount of error.
Find the percent error.
percent error =
=
= 0.1 or 10%
Substitution
Simplify.
So, the percent error is 10%.
15 feet – 13.5 feet = 1.5 feet

15. Answer
Need Another Example?
Morgan estimates that it will take 12 minutes
to download a movie from an online movie
store. It actually took 15.5 minutes to
download the movie. Find the percent error.
Round to the nearest whole percent if
necessary.
23%

16. How did what you learned
today help you answer the
HOW can percent help you understand
situations involving money?
Course 2, Lesson 2-5
Ratios and Proportional Relationships

17. How did what you learned
today help you answer the
HOW can percent help you understand
situations involving money?
Course 2, Lesson 2-5
Ratios and Proportional Relationships
Sample answers:
• You can find the percent of change in the in a real-
world situation involving money.
• You can find the percent error in the estimated cost of
an item compared to the actual cost.

18. The next lesson involves
solving problems involving
sales tax, tips, and markup.
How do you think what you
learned today will connect
with the next lesson?
Ratios and Proportional RelationshipsRatios and Proportional Relationships
Course 2, Lesson 2-5