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2.07 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.

21

A stockbroker bought 316 shares at \$23.25 per share and later sold the shares for a total of\$15\,281.

a

Calculate the total amount the stockbroker paid for the 316 shares.

b

Calculate the profit earned by the stockbroker.

c

Calculate the percentage profit to two decimal places.

Profit and loss
22

Justine bought a plasma TV for \$3720 and later sold it for \$3590.

a

Express the loss as a percentage of the cost price, correct to one decimal place.

b

Express the loss as a percentage of the sale price, correct to one decimal place.

23

Luke buys a used bike for \$385 and resells it for \$560 without spending any money on it.

a

How much profit did Luke make on the bike?

b

Calculate Luke's percentage profit, correct to two decimal places.

24

Sally purchased a dress for \$20 and auctioned it online for \$41. Calculate:

a

The profit as a percentage of the cost, correct to two decimal places.

b

The profit as a percentage of the revenue, correct to two decimal places.

25

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.
26

Amelia bought a truck for \$17\,300 and sold it four years later, making a loss of 25\%. How much did she sell it for?

27

Ananya invests \$8000 in the stock market only to see her shares plummet in value to \$2423.

a

Find the amount of Ananya's loss.

b

Find her percentage loss, correct to two decimal places.

28

At the beginning of the year, a car manufacturer’s share price starts at \$9.70. Over the course of the year, the share price drops by \$1.80. If Neil bought 100 shares, find:

a

The total loss.

b

The percentage loss, correct to two decimal places.

29

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.
30

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

31

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?

32

In a fire sale, a store sold goods at 41\% below cost price. If \$13\,900 was earned from the sale, calculate:

a

The original cost of goods sold.

b

The loss on the sale.

33

Given that an item is sold for 1.5 times its cost price, calculate the percentage profit of the sale.

34

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.

35

If a business that was bought last year is now sold for a 15\% profit, find the simplified ratio of selling price to buying price.

36

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.

37

A pair of socks costs a salesman \$1.69 to make. He is then taxed 25\% of the profit he makes from the sale. He sells each pair of socks for \$P.

a

Write an expression in terms of P, for his profit per pair of socks:

i

Before tax.

ii

After tax.

b

The salesman wishes to make an after tax profit of 33\%. Calculate the price, \$P, at which he must sell each pair of socks.

38

Dave bought a unique number plate as an investment. He sold it to a car owner at 11\% profit, who then sold it to an interstate buyer at 2\% profit. If the interstate buyer bought it for \$3500, how much did Dave pay for the number plate?

Graphs of percentage change
39

The following graph shows a breakdown of the methods by which music was acquired in 2010 and 2011:

a

What percentage of unpaid acquired music in 2011 came through the following. Round your answer to the nearest whole percentage.

i

Peer-to-peer filesharing.

ii

Digital lockers.

iii

Online piracy.

iv

Offline swapping.

b

Did the majority of music acquired come from unpaid or paid sources?

c

Did the majority of unpaid music come through offline swapping or online piracy?

40

The given graph shows a breakdown of worldwide motion picture industry losses (in millions of dollars) in 2015:

(Source: Motion Picture Association and LEK Consulting)

a

What was the total piracy cost in 2015?

b

What percentage of the total worldwide piracy costs did US piracy costs make up? Round your answer to the nearest whole percentage.

c

What percentage of the total worldwide piracy costs did non-US hard goods piracy costs make up? Round your answer to the nearest whole percentage.

d

What percentage of the total worldwide piracy costs did worldwide illegal downloading make up? Round your answer to the nearest whole percentage.

e

What percentage of the total worldwide piracy costs did worldwide hard goods piracy make up? Round your answer to the nearest whole percentage.

41

The following charts show the demographics of worldwide movie pirates:

(Source: Motion Picture Association and LEK Consulting)

Use the graphs to describe a typical movie pirate.

42

The given graph shows a breakdown of worldwide box office revenue (in billions of dollars) from 2006-2010:

a

What was the worldwide box office revenue in 2010?

b

What was the US and Canadian box office revenue in 2006?

c

What was the international (non-US and Canadian) box office revenue in 2008?

d

What was the size of the percentage increase in worldwide box office revenue from 2006 to 2010? Round your answer to the nearest whole percentage.

e

What was the size of the percentage increase in US and Canadian box office revenue from 2006 to 2010? Round your answer to the nearest whole percentage.

f

Did the worldwide box office revenue increase or decrease from 2006 to 2010?

g

Find the percentage change in global recorded musical sales revenue for the period between 2000 and 2010. Round your answer to one decimal place.

2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
\text{Year}
12
14
16
18
20
22
24
26
\text{Revenue (in billions }\$)

(Source: International Federation of the Phonographic Industry)

h

Explain why you think the box office revenue and music sales revenue have such different trends leading up to 2010.

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Outcomes

ACMEM012

determine one amount expressed as a percentage of another

ACMEM013

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

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