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2.06 Solve problems with percentages

Worksheet
Discounts
1

Steph is going to buy a hat that is marked as 25\% off. The original price was \$36.

a

What is the value of the discount?

b

What is the price that Steph will pay for the hat?

2

Paul is going to buy an eraser from a stationery store that is having a storewide 10\% off sale. The original price of the eraser was \$6.

a

What is the value of the discount?

b

What is the price that Paul will pay for the eraser?

3

A movie ticket usually costs \$21 but staff are given a 40\% discount.

a

How much less do staff pay for a ticket?

b

What price do staff pay for a ticket?

4

The full price is \$300. Yvonne receives a discount of 55\%.

a

How much would a 10\% discount be?

b

How much would a 5\% discount be?

c

Hence, find the discount that Yvonne received.

5

Emma is going to purchase some sports gear on layby. This involves paying some money as a deposit and paying the remainder later. The amount of the layby is \$100.

a

If the amount the store needs as a deposit is 50\%, calculate the amount of the deposit.

b

Calculate the remaining balance on the layby.

6

A store is offering a 20\% discount on all goods. Ivan purchases a fridge with an original price of \$640 and a stove with an original price of \$840.

a

Without the discount, how much would Ivan have to pay altogether?

b

Calculate the discount amount that Ivan receives for the fridge.

c

Calculate the discount amount that Ivan receives for the stove.

d

Calculate the total discount amount that Ivan receives.

e

Find the amount Ivan pays for the goods after the discount.

7

Jenny is going to buy a ruler from a stationary store that is having a 50\% off everything sale. The original price was \$5.

a

What is the value of the discount?

b

What is the price that Jenny will pay for the ruler?

8

Bart receives a 20\% discount off a bill for paying cash.

a

What percentage of the bill does Bart pay?

b

Calculate the amount Bart pays if the original bill was \$65.

9

An item with an original price of \$230 is sold at a discount of \$69.

a

Calculate the discount rate.

b

Find the sales price.

10

A tennis racket marked at a price of \$150 is advertised to be selling at 10\% off the marked price.

a

Find the amount of the discount on the tennis racket.

b

Find the discounted price of the tennis racket.

11

A music store advertises 12\% off all CDs and DVDs. A CD is normally priced at \$16.

a

Find the amount of the discount on this CD.

b

Find the discounted price of the CD.

12

Two book sellers advertised a sale:

  • Honest Anne offered 20\% off the original price of her books.

  • Fair Freddie offered up to 50\% off the original price of his books.

a

Fiona bought books from Honest Anne. The total original price of her books was \$130. Find the value of the discount she received?

b

How much did Fiona pay Honest Anne for the books?

c

At Fair Freddie's, Sarah bought the same books as Fiona at the same original price. She was given 10\% off on the first \$100 worth of books, and 50\% off for the remainder of the original price.

Find the total discount Sarah received on her purchase.

d

What amount did Sarah pay Fair Freddie for the books?

e

Who paid the cheapest price: Fiona or Sarah?

13

A holiday resort in Tasmania reduced its overnight rates from \$232 to \$120.

a

Find the value of the discount.

b

Find the percentage discount on the original price. Round your answer to two decimal places.

14

During a sale period, there is 50\% off on a blouse whose original price was \$674.

a

Find the value of the discount.

b

Find the sale price of the blouse.

15

A game retailer sells new games at a markup of 33\% above the cost price and old games at a markup of 18\%. Calculate the selling price of:

a

The newly released Super Zora 5 game which has a cost price of \$90.

b

The old Super Zora 3 game which has a cost price of \$31.

Earnings
16

A sales assistant is paid a commission of 15\% on his weekly sales. Find his commission for a week in which he sells products to the value of \$2000.

17

Maria and Eileen are employed by different companies to sell computers. Their commissions on weekly sales are 4.5\% and 5\%, respectively. This week they each sold \$13\,600 worth of computers.

a

Find Maria's commission for the week.

b

Find Eileen's commission for the week.

c

Who received the higher commission and by how much?

18

A woman is paid a commission of 9\% on her weekly sales. If her total commission for the week was \$541, calculate:

a

The value of 1\% of her sales.

b

The total value of her sales for that week to the nearest dollar.

19

If person earns a \$1160 commission for \$14\,500 in total sales, calculate their commission rate as percentage.

20

Luke deposits \$8635 in a bank for one year. The interest rate of the bank is 7\% p.a.

a

How much interest, did Luke earn for the year?

b

Find the total amount in his bank account at the end of the year.

Profit and loss
21

Every item in store is sold at 8\% more than its cost. If a product was bought from the manufacturer for \$360, calculate:

a
The sale price.
b
The profit.
22

Every item in store is sold at 9\% more than its cost. If a product is sold for \$110, calculate:

a

The cost price.

b
The profit.
23

An investor sold his portfolio at 9\% profit for a price of \$2000. Calculate the original value of his portfolio.

24

A manufacturer is selling its old factory machinery for \$24\,920, which represents a loss of 39\%. How much did the manufacturer purchase the machinery for?

25

The value of a car depreciated by 5\% this year. If its value at the start of the year was \$4000:

a

By how much did it depreciate by?

b

Calculate the current value of the car.

26

Lynne bought a property for \$371\,000. In the first year, it increased in value by 12\%, but in the second year, it decreased in value by 6\%. The running costs during the two years amounted to \$1500.

a

Calculate the amount Lynne earned from the changing value of the property.

b

Hence, calculate Lynne's total profit.

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Outcomes

1.1.13

calculate a percentage of a given amount, using mental/written strategies or technology when appropriate

1.1.14

determine one amount expressed as a percentage of another

1.1.15

apply percentage increases and decreases in situations, for example, mark-ups and discounts and GST

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