SAT MATH - PERCENTS AND EQUATIONS

Translate each verbal phrase into an algebraic equation and solve.

Example 1 :

What is 0.3% of 4?

Solution :

Let x be 0.3% of 4.

Wite an equation from the given information.

x = 0.3% of 4

Write the 0.3% as a fraction.

x = (⁰^.³⁄₁₀₀)4

Simplify.

x = ¹^.²⁄₁₀₀

x = 0.012

Therefore, 0.3% of 4 is 0.012

Example 2 :

What percent of 30 is 5?

Solution :

Let x percent 30 be 5.

Wite an equation from the given information.

x% of 30 = 5

Write the x% as a fraction.

(ˣ⁄₁₀₀)30 = 5

Simplify.

³ˣ⁄₁₀ = 5

Multiply both sides by 10.

3x = 50

Divide both sides by 3.

x = ⁵⁰⁄₃

Therefore, ⁵⁰⁄₃ percent of 30 is 5.

Example 3 :

64 is 250% of what number?

Solution :

Let 64 be 250% of x.

Wite an equation from the given information.

64 = 250% of x

Write the 250% as a fraction.

64 = (²⁵⁰⁄₁₀₀)x

Simplify.

64 = (⁵⁄₂)x

Multiply both sides by 2.

128 = 5x

Divide both sides by 5.

25.6 = x

Therefore, 64 is 250% of the number 25.6.

Solved Problems

Problem 1 :

28% of what number is 7?

Solution :

Let 28% of x be 7.

28% of x = 7

0.28x = 7

x = 25

Therefore, 28% of 25 is 7.

Problem 2 :

3.6 is 240% of what number?

Solution :

Let 3.6 be 240% of x.

3.6 = 240% of x

3.6 = 2.4x

1.5 = x

Therefore, 3.6 is 240% of 1.5.

Problem 3 :

½% of 180 is what number?

Solution :

Let ½% of 180 be x.

½% of 180 = x

0.5% of 180 = x

0.005 ⋅ 180 = x

0.9 = x

Therefore, ½% of 180 is 0.9.

Problem 4 :

3⅓% of what number is 2.5?

Solution :

Let 3⅓% of x be 2.5.

3⅓% of x = 2.5

(¹⁰⁄₃)(¹⁄₁₀₀)x = 2.5

(¹⁄₃₀)x = 2.5

x = 75

Therefore, 3⅓% of 75 is 2.5.

Problem 5 :

26.4 is 0.55% of what number?

Solution :

Let 26.4 be 55% of x.

26.4 = 0.55% of x

26.4 = 0.0055x

4800

Therefore, 26.4 is 0.55% of 4800.

Problem 6 :

What percent of 12 is 8?

(A)  60%

(B)  66⅔%

(C)  75%

(D)  130⅓%

Solution :

Let x percent of 12 be 8.

x% of 12 = 8

(ˣ⁄₁₀₀)12 = 8

³ˣ⁄₂₅ = 8

x = ²⁰⁰⁄₃

x =  66⅔

66⅔ percent of 12 is 8.

Therefore, the correct answer is option (B).

Problem 7 :

54 is 120% of k.

Which of the following equations can be used to solve the above expression?

(A)  ¹⁰⁰⁄₁₂₀ = ⁵⁴⁄k

(B)  ⁵⁴⁄₁₀₀ = ¹²⁰⁄k

(C)  ¹⁰⁰⁄₅₄ = ¹²⁰⁄k

(D)  ¹²⁰⁄₁₀₀ = ⁵⁴⁄k

Solution :

54 is 120% of k

54 = (¹²⁰⁄₁₀₀)k

⁵⁴⁄k = ¹²⁰⁄₁₀₀

¹²⁰⁄₁₀₀ = ⁵⁴⁄k

Therefore, the correct answer is option (D).

Problem 8 :

If Kevin’s monthly salary of $4,500 is 72 percent of Paul’s monthly salary, what is Paul’s monthly salary?

(A)  $3,240

(B)  $5,150

(C)  $5,870

(D)  $6,250

Solution :

Given : Kevin’s monthly salary of $4,500 is 72 percent of Paul’s monthly salary.

Let x be Paul's monthly salary.

From the given information,

4500 = 72% of x

4500 = 0.72x

6250 = x

Paul's monthly salary is $6,250.

Therefore, the correct answer is option (D).

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