Worksheet: Percentage Equations

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In this worksheet, we will practice finding the part given its percentage and the whole or vice versa and solving problems involving percentage using proportions.

Q1:

Fill in the missing value: % of 50 is 22.

Q2:

In a family, 21 out of 25 members are female. What percentage of the family are female?

Q3:

Isabella collects stickers. With her allowance, she buys 5 stickers each week. She has worked out that her number of stickers will have increased by 20% after six weeks. How many stickers does she have now?

Q4:

Write an equation to represent 23% of 619, and then solve it to the nearest tenth.

  • A 𝑛 ⋅ 0 . 2 3 = 6 1 9 , 𝑛 = 2 6 9 . 1
  • B 𝑛 = 0 . 2 3 ⋅ 6 1 9 , 𝑛 = 1 4 2 . 4
  • C 𝑛 ⋅ 2 3 = 6 . 1 9 , 𝑛 = 3 . 7
  • D 𝑛 = 2 . 3 ⋅ 6 1 9 , 𝑛 = 1 4 . 2
  • E 𝑛 ⋅ 2 3 = 0 . 6 2 , 𝑛 = 3 7 . 2

Q5:

Let 𝑛 be the percentage representing 260.7 out of 𝑡ℎ𝑟𝑒𝑒ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑠𝑒𝑣𝑒𝑛𝑡𝑦−𝑓𝑖𝑣𝑒. Write an equation for 𝑛 and then solve it. Round the percentage to one decimal place.

  • A 𝑛 ⋅ 2 6 0 . 7 = 3 7 5 , 𝑛 = 1 4 . 4 %
  • B 𝑛 = 2 6 0 . 7 ⋅ 3 7 5 , 𝑛 = 9 . 8 %
  • C 𝑛 ⋅ 3 7 5 = 2 6 0 . 7 , 𝑛 = 6 9 . 5 %
  • D 𝑛 ⋅ 3 7 5 = 2 6 0 . 7 , 𝑛 = 7 . 0 %
  • E 𝑛 = 2 6 0 . 7 ⋅ 3 7 5 , 𝑛 = 9 7 . 8 %

Q6:

During target practice, an archer shot 389 arrows. If 23.3% of his arrows hit the bullseye, determine, to the nearest whole number, how many arrows struck the bullseye.

Q7:

Write an equation that represents 0.5% of 84.8, and then solve it to the nearest tenth.

  • A 𝑛 ⋅ 0 . 5 = 0 . 8 4 8 , 𝑛 = 1 . 7
  • B 𝑛 8 4 . 8 = 0 . 5 , 𝑛 = 4 2 . 4
  • C 𝑛 ⋅ 0 . 5 1 0 0 = 8 4 . 8 , 𝑛 = 1 7 . 0
  • D 𝑛 8 4 . 8 = 0 . 5 1 0 0 , 𝑛 = 0 . 4
  • E 𝑛 ⋅ 0 . 5 = 0 . 0 8 4 8 , 𝑛 = 0 . 2

Q8:

Scarlett would like a 25% concentration of sulfuric acid. She has 10 liters of 10% concentration. How much pure sulfuric acid must be added to the 10% concentration?

Q9:

Fill in the missing value: 614% of =25.

Q10:

According to some studies, in the last century ninety percent of lions have disappeared in Africa due to habitat loss, hunting, loss of prey, and other factors. Today, there are only about 20,000 lions in Africa; they are extinct in 26 African countries. How many lions were in Africa 100 years ago?

Q11:

Fill in the missing value: 27% of 500 is 15% of .

Q12:

Increase 200 by 16%.

Q13:

Victoria bought a coat 10% off its original price. She paid $36. The given diagram can be used to find the shirt’s original price.

When dividing the shaded area into 90 equal parts, what does each part represent in dollars?

When dividing the shaded area into 90 equal parts, what does each part represent as a percent?

  • A 9 0 % of the original price
  • B 1 . 1 1 % of the original price
  • C 9 % of the original price
  • D 1 % of the original price

Q14:

Daniel and Victoria sold their car for $700 less than the amount they bought it for three years ago. This corresponds to a depreciation of 35%. The diagram depicts this situation, where the shaded area represents the loss of value of their car.

If the shaded area is divided into 35 equal parts, what does each part represent in dollars and percent?

  • A $ 8 0 , 10%
  • B $ 8 0 , 1%
  • C $ 2 0 , 1%
  • D $ 2 0 , 10%
  • E $ 3 5 , 1%

Since we know that 35% of the original price 𝑥 of the car corresponds to $700, the diagram can be redrawn to show that 35 and 100 are in the same proportion as 700 and the original price of the car.

Which of the following relationships does NOT correspond to the diagram?

  • A 𝑥 7 0 0 = 1 0 0 3 5
  • B 3 5 7 0 0 = 1 0 0 𝑥
  • C 3 5 1 0 0 = 7 0 0 𝑥
  • D 7 0 0 3 5 = 𝑥 1 0 0
  • E 7 0 0 1 0 0 = 𝑥 3 5

How much did they pay for their car three years ago?

Q15:

A vase contains some flowers. 20% of the flowers are pink, 48% of the flowers are violet, and the rest are red. Given that the vase contains 10 pink flowers, calculate how many violet flowers and how many red flowers it contains.

  • Aviolet flowers =24, red flowers =16
  • Bviolet flowers =24, red flowers =26
  • Cviolet flowers =48, red flowers =52
  • Dviolet flowers =48, red flowers =42

Q16:

Last month, the amount that Michael spent on transportation was 88% of the amount he spent on utilities. If he spent $550 on transportation, determine the amount he spent on utilities.

Q17:

The price of a mobile phone is 550 LE. After a 42% discount, how much will the phone cost?

Q18:

The UK held a referendum on whether, or not, to remain a member of the European Union in 2,016. 17,410,742 people voted to leave the EU, and 16,141,241 voted to remain in the EU. This represented a turnout of 72.15% of eligible voters, rounded to 2 decimal places. Using these figures, calculate how many people were eligible to vote in the referendum, giving your answer correct to four significant figures.

Q19:

A man bought a washing machine for 4,396 LE, then spent a further 640 LE to repair it. He then sold the machine, making a 50% loss on the total amount of money he had spent on buying and repairing it. What price did he sell the washing machine for and how much money did he lose?

  • A5,036 LE, 2,518 LE
  • B2,518 LE, 2,518 LE
  • C1,878 LE, 2,518 LE
  • D7,554 LE, 2,518 LE

Q20:

A person bought a TV set using a 50% discount voucher. Given that the full price was 804 LE, how much did the person pay?

Q21:

Liam pays $70 each month for his gym subscription. Due to inflation, this amount will increase by 8% from next month. How much will Liam pay per month after the increase?

Q22:

A school produced 450 pounds of garbage in a month. If the school wants to reduce the weight of garbage produced in the following month to 79% of its weight, what should the target weight be?

Q23:

A farmer spent 809 LE on buying a goat and spent 81 LE feeding the goat until it was old enough to sell. The goat was sold for 85% more than the total of the cost and feed. How much did the goat sell for?

Q24:

A store manager sold a refrigerator for 2,964 LE. Given that a 20% profit was made, how much did the store manager buy the refrigerator for?

Q25:

Ethan saves 40% of his allowance each week. If he saves $84 in 3 weeks, determine his weekly allowance.

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