# 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:

- \(0.9x+20=830\)
- \(0.9(x-20)=830\)

- Decide which equation represents each story.
- Explain why one equation has parentheses and the other doesn’t.
- 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:

(From Unit 2, Lesson 7.)
1 to 1,000,000

### 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?