Lesson 8Percent Increase and Decrease with Equations
Learning Goal
Let’s use equations to represent increases and decreases.
Learning Targets
I can solve percent increase and decrease problems by writing an equation to represent the situation and solving it.
Lesson Terms
- percentage decrease
- percentage increase
Warm Up: From 100 to 106
Problem 1
How do you get from one number to the next using multiplication or division?
Activity 1: Interest and Depreciation
Problem 1
![A photo of a new red car.](../../../../../../embeds/b9e18eb1--7.4.new.car.png)
![A photo of the same car now older and damaged.](../../../../../../embeds/79ca598b--7.4.old.car.png)
Money in a particular savings account increases by about 6% after a year. How much money will be in the account after one year if the initial amount is $100? $50? $200? $125?
dollars? If you get stuck, consider using diagrams or a table to organize your work. The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial value was $1,000? $5,000? $5,020?
dollars? If you get stuck, consider using diagrams or a table to organize your work.
Activity 2: Matching Equations
Problem 1
Match an equation to each of these situations. Be prepared to share your reasoning.
The water level in a reservoir is now 52 meters. If this was a 23% increase, what was the initial depth?
The snow is now 52 inches deep. If this was a 77% decrease, what was the initial depth?
Are you ready for more?
Problem 1
An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram sample of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour.
How much goo will she have after 1 hour? After 2 hours? After 3 hours? After
hours? When she put the goo in the dark, it shrank by 75% every hour. How many hours will it take for the goo that was exposed to light for
hours to return to the original size?
Activity 3: Representing Percent Increase and Decrease: Equations
Problem 1
The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s tank hold?
Explain why this situation can be represented by the equation
Problem 2
Write an equation to represent each of the following situations.
A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold?
After a 25% discount, the price of a T-shirt was $12. What was the price before the discount?
Compared to last year, the population of Boom Town has increased by 25%.The population is now 6,600. What was the population last year?
Lesson Summary
We can use equations to express percent increase and percent decrease. For example, if
![A tape diagram with a 2 segments, one blue and a shorter white one. The blue segment is labeled "x" and the white is "0.15x". The whole diagram is "1.15x"](../../../../../../embeds/3bfea72a--7.4.8.revised.image.01.png)
we can represent this using any of these equations:
So if someone makes an investment of
Here is another example: if
![A tape diagram labeled b with 2 segments, one white and a longer blue one. The blue is labeled "0.93b" and the white is "0.07b"](../../../../../../embeds/78fb6678--7.4.8.revised.image.02.png)
we can represent this using any of these equations:
So if the amount of water in a tank decreased 7% from its starting value of
Often, an equation is the most efficient way to solve a problem involving percent increase or percent decrease.