# Lesson 12

Solving Problems about Percent Increase or Decrease

### Problem 1

Select **all** expressions that show \(x\) increased by 35%.

\(1.35x\)

\(\frac{35}{100}x\)

\(x + \frac{35}{100}x\)

\(( 1+0.35)x\)

\(\frac{100+35}{100}x\)

\((100 + 35)x\)

### Solution

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### 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.

### Solution

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### Problem 3

Select **all** the expressions that are the result of decreasing \(x\) by 80%.

\(\frac{20}{100}x\)

\(x - \frac{80}{100}x\)

\(\frac{100-20}{100}x\)

\(0.80x\)

\((1-0.8)x\)

### Solution

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### Problem 4

Which scale is equivalent to 1 cm to 1 km?

1 to 1000

10,000 to 1

1 to 100,000

100,000 to 1

1 to 1,000,000

### Solution

### 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?