# Lesson 12

Solving Problems about Percent Increase or Decrease

Let’s use tape diagrams, equations, and reasoning to solve problems with negatives and percents.

### Problem 1

Select all expressions that show $$x$$ increased by 35%.

A:

$$1.35x$$

B:

$$\frac{35}{100}x$$

C:

$$x + \frac{35}{100}x$$

D:

$$( 1+0.35)x$$

E:

$$\frac{100+35}{100}x$$

F:

$$(100 + 35)x$$

### Problem 2

Here are two stories:

• The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class.
• A store reduces the price of a computer by $20. Then during a 10% off sale, a customer pays$830.

Here are two equations:

• $$0.9x+20=830$$
• $$0.9(x-20)=830$$
1. Decide which equation represents each story.
2. Explain why one equation has parentheses and the other doesn’t.
3. Solve each equation, and explain what the solution means in the situation.

### Problem 3

Select all the expressions that are the result of decreasing $$x$$ by 80%.

A:

$$\frac{20}{100}x$$

B:

$$x - \frac{80}{100}x$$

C:

$$\frac{100-20}{100}x$$

D:

$$0.80x$$

E:

$$(1-0.8)x$$

### Problem 4

Which scale is equivalent to 1 cm to 1 km?

A:

1 to 1000

B:

10,000 to 1

C:

1 to 100,000

D:

100,000 to 1

E:

1 to 1,000,000

(From Unit 2, Lesson 7.)

### Problem 5

Triangle $$DEF$$ is a right triangle, and the measure of angle $$D$$ is $$28^\circ$$. What are the measures of the other two angles?

(From Unit 1, Lesson 13.)