# SOLVING PERCENT PROBLEMS WORKSHEET

Problem 1 :

What is 25% of 80?

Problem 2 :

70 is what percent of 280?

Problem 3 :

20% of x is equal to 30% of y, solve for x in terms y.

Problem 4 :

If x is equal to 25% of y, what is the value of ˣ⁄y?

Problem 5 :

The cost price of a product \$60. If the product is sold at a profit of 15%, what is the selling price of the product?

Problem 6 :

The cost price of a product \$80. If the product is sold at a loss of 5%, what is the selling price of the product?

Problem 7 :

The selling price of a product \$125. If the product is sold at a profit of 12%, what is the cost price of the product?

Problem 8 :

The selling price of a product \$135.80. If the product is sold at a loss of 3%, what is the cost price of the product?

Problem 9 :

Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?

Problem 10 :

A book was on sale for 40% off its original price. If the sale price of the book was \$18.00, what was the original price of the book? (Assume there is no sales tax.)

Problem 11 :

A photocopy machine is initially loaded with 5,000 sheets of paper. The machine starts a large job and copies at a constant rate. After 20 minutes, it has used 30% of the paper. Which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing?

Problem 12 :

Gisela would owe \$15,500 in taxes each year if she were not eligible for any tax deductions. This year, Gisela is eligible for tax deductions that reduce the amount of taxes she owes by \$2,325.00. If these tax deductions reduce the taxes Gisela owes this year by d%, what is the value of d? Let x be the value which is equal to 25% of 80.

x = 25% of 80

x = 0.25 ⋅ 80

x = 20

25% of 80 is 20.

Let 70 be x% of 280.

70 = x% of 280

70 = ˣ⁄₁₀₀ ⋅ 280

Divide both sides by 280.

0.25 = ˣ⁄₁₀₀

Multiply both sides by 100.

25 = x

Therefore, 70 is 25% of 280.

20% of x = 30% of y

0.2x = 0.3y

(²⁄₁₀) = (³⁄₁₀)y

Divide both sides by 10.

2x = 3y

Divide both sides by 2.

x = ³ʸ⁄₂

x = 25% of y

x = 0.25y

Divide both sides y.

ˣ⁄y = 0.25

ˣ⁄y = ¼

selling price = (100 + 15)% of cost price

Substitute \$60 for cost price.

selling price = (100 + 15)% of cost price

= 115% of \$60

= 1.15 ⋅ \$60

= \$69

selling price = (100 - 5)% of cost price

Substitute \$60 for cost price.

selling price = (100 - 5)% of cost price

= 95% of \$80

= 0.95 ⋅ \$80

= \$76

(100 + 12)% of cost price = selling price

Substitute \$125 for selling price.

112% of cost price = \$125

1.12 ⋅ cost price = \$125

Divide both sides by 1.12.

cost price = \$140

(100 - 3)% of cost price = selling price

Substitute \$174.60 for selling price.

97% of cost price = \$174.60

0.97 ⋅ cost price = \$174.60

Divide both sides by 0.97.

cost price = \$180

The selling price of a product \$135.80. If the product is sold at a loss of 3%, what is the cost price of the product?

8 hours = 8 ⋅ 60 minutes

8 hours = 480 minutes

15% of 8 hours :

= 15% of 480 minutes

= 0.15 ⋅ 480 minutes

= 72 minutes

Lani spent 72 minutes of her workday in meeting.

Let x be the original price of the book.

Given : After 40% off the original price, the sale price of the book was \$18.00.

(100 - 40)% of x = 18

60% of x = 18

0.6x = 18

Divide each side by 0.6.

x = 30

The original price of the book was \$30.

Number of sheets used in 20 minutes :

= 30 % of 5000

= 0.3 ⋅ 5000

= 1500

Number of sheets used in 1 hour (3 times 20 minutes) :

⋅ 1500

= 4500

Number of sheets remaining after 1 hour :

= 5000 - 4500

= 500

The number of paper sheets remaining in the machine after 1 hour is 1500.

Given : Deductions reduce the original amount of taxes owed by \$2,325.00.

Because the deductions reduce the original amount of taxes owed by d%, the equation shown below can be used to find this percent decrease, d.

ᵈ⁄₁₀₀ = ²³²⁵⁄₁₅₅₀₀

Simplify.

ᵈ⁄₁₀₀ = ²³²⁵⁄₁₅₅₀₀

Multiply each side by 100.

d = 15

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