SAT MATH - PERCENT OF CHANGE

Example 1 :

Write the following decimal as a percent.

0.65

Solution :

= 0.65

Multiply the decimal by 100 and add the % sign.

= 0.65 ⋅ 100%

Since 0.65 is multiplied by 100, move the decimal point two digits to the right.

= 65%

Example 2 :

Write the following fraction as a percent.

³⁄₁₆

Solution :

= ³⁄₁₆

Multiply the decimal by 100 and add the % sign.

= ³⁄₁₆ ⋅ 100%

Since ³⁄₁₆ is multiplied by 100, move the decimal point two digits to the right.

= ³⁰⁰⁄₁₆%

= 18.75%

Example 3 :

Write 175% as a decimal and a fraction.

Solution :

= 175%

Multiply the amount of percent by ¹⁄₁₀₀.

= 175 ⋅ (¹⁄₁₀₀)

= ¹⁷⁵⁄₁₀₀

Simplify.

= ⁷⁄₄

Example 4 :

A $300 tablet is on sale for $234. What is the percent of discount?

Solution :

Percent of discount :

= 22%

Example 5 :

The population of Sunny Hills increased from 12,000 to 15,840 in ten years. What is the percent increase of the population?

Solution :

Percent of increase :

= 0.32 ⋅ 100%

= 32%

Solved Problems

Problem 1 :

Which of the following is equivalent to 0.03% of 4?

(A)  0.12

(B)  0.012

(C)  0.0012

(D)  0.00012

Solution :

= 0.03% of 4

= 0.03 ⋅ ¹⁄₁₀₀ ⋅ 4

= ⁰^.¹²⁄₁₀₀

= 0.0012

Therefore, the correct answer is option (C).

Problem 2 :

Which of the following is equivalent to ¹⁄₄₀₀?

(A)  0.25%

(B)  0.025%

(C)  0.0025%

(D)  0.00025%

Solution :

= ¹⁄₄₀₀

= ¹⁄₄₀₀ ⋅ 100%

= ¹⁄₄ %

= 0.25%

Therefore, the correct answer is option (A).

Problem 3 :

The quantities x and y are positive. If x is decreased by 20 percent and y is increased by 20 percent, then the product of x and y is

(A)  unchanged

(B)  decreased by 4%

(C)  increased by 4%

(D)  decreased by 4%

Solution :

x is decreased by 20 percent :

= x - 20% of x

= x - 0.2x

= 0.8x

y is increased by 20 percent :

= y + 20% of y

= y + 0.2y

= 1.2y

Product :

= 0.8x ⋅ 1.2y

= 0.96(xy)

= 0.96 ⋅ ¹⁄₁₀₀% ⋅ xy

= 96% of xy

So, the product is decreased by 4 percent.

Therefore, the correct answer is option (B).

Problem 4 :

By what percent is 4.5 ⋅ 10⁵ greater than 9 ⋅ 10⁴?

(A)  200%

(B)  400%

(C)  500%

(D)  600%

Solution :

Find what percentage of 9 ⋅ 10⁴ equal to 4.5 ⋅ 10⁵.

Let x% of 9 ⋅ 10⁴  be qual to 4.5 ⋅ 10⁵.

x%(9 ⋅ 10⁴) = 4.5 ⋅ 10⁵

(ˣ⁄₁₀₀)(9 ⋅ 10⁴) = 4.5 ⋅ 10⁵

x(9 ⋅ 10²) = 4.5 ⋅ 10⁵

Problem 5 :

The temperature increased from 60°F to 72°F. What is the percent increase in temperature?

(A)  15%

(B)  ⁵⁰⁄₃%

(C)  20%

(D)  ⁷⁰⁄₃%

Solution :

Percent increase in temperature :

= 20%

Therefore, the correct answer is option (C).

Problem 6 :

This year’s enrollment in Mesa School District is 6,000, which is 20 percent higher than last year’s. What was last year’s enrollment in Mesa School District?

Solution :

Let x be the last year’s enrollment in Mesa School District.

Given : This year’s enrollment in Mesa School District is 6,000, which is 20 percent higher than last year’s.

x + 20% of x = 6000

x + 0.2x = 6000

1.2x = 6000

x = 5000

Last year’s enrollment in Mesa School District was 5,000.

Problem 7 :

If 125% of x is 80 and x is n% of 400, what is the value of n?

Solution :

Given : 125% of x is 80.

125% of x = 80

(¹²⁵⁄₁₀₀)x = 80

(⁵⁄₄)x = 80

x = 64

Given : x is n% of 400.

x = (ⁿ⁄₁₀₀)400

x = 4n

Substitute x = 64.

64 = 4n

16 = n

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