Middle Years

# 4.08 Consumer percentages

Worksheet
Mark ups and discounts
1

Find the discounted price for each of the following:

a

A pair of boots priced at \$80 is discounted by 35\%. b A desk priced at \$80 is discounted by 40\%.

c

A board game priced at \$25 is discounted by 30\%. d A cricket bat originally marked at a price of \$150 is advertised to be selling at 45\% off this marked price.

2

Find the marked up price for each of the following:

a

A book priced at \$90 is marked up by 40\%. b A dress at \$120 is marked up by 30\%.

c

A brush set priced at \$140 is marked up by 45\%. d A t-shirt originally priced at \$170 is marked up to sell for 45\% more.

3

Find the percentage increase in price after the following mark ups are applied:

a

The new price of a wallet after a mark up is calculated by multiplying the original price by 110\%.

b

The new price of a hat after a mark up is calculated by multiplying the original price by 121\%.

4

Find the percentage decrease in price after the following discounts are applied:

a

The new price of a phone after a discount is calculated by multiplying the original price by 95\%.

b

The new price of a shirt after a discount is calculated by multiplying the original price by 77\%.

5

Find the original price of the following items:

a

The price of a basketball was marked up by 60\% and is now \$144. b The price of a singlet was marked up by 45\% and is now \$26.10.

c

The price of a backpack was discounted by 30\% and is now \$63. d The price of a golf club was discounted by 35\% and is now \$11.70.

6

Find the original price of the following items:

a

A shop owner decides to mark up the price of a sled by 31\% so that it now sells for exactly \$60. b A bakery sells garlic twist loaves, baked fresh every day. At 4:30 pm, just before closing, they discount any remaining loaves by 43\% and sell them for \$2 each.

7

A popular hotel increased its nightly rates from \$277 to \$349.

a

Calculate how much more a single night's stay costs after the price increase.

b

By what percentage did the nightly rate increase? Round your answer to two decimal places.

8

A holiday resort in Tasmania reduced its overnight rates from \$313 to \$239.

a

Calculate how much less a single nights stay cost after the decrease in price.

b

By what percentage did the nightly rate decrease? Round your answer to two decimal places.

Multiple mark ups and discounts
9

A laptop originally sells at \$4700. a Calculate its sale price after successive discounts of 6\% and 9\%. b Calculate its sale price after successive discounts of 9\% and 6\%. c Does the order of discounting affect the sale price? Explain your answer. d Calculate its sale price after successive discounts of 8\%, 7\% and 5\%. 10 Find the final price after applying both mark ups: a A mattress originally priced at \$90 is marked up by 70\%. A few months later, the mattress is marked up from its new price by a further 60\%.

b

A world trip originally priced at \$9000 is marked up by 17\%. A few months later, the world trip is marked up from its new price by a further 49\%. 11 Find the final price after applying both discounts: a A painting canvas originally priced at \$80 is discounted by 40\%. A few months later, the painting canvas is discounted from its new price by a further 20\%.

b

A second-hand boat originally priced at \$12\,000 is discounted by 23\%. A few months later, the boat is discounted from its new price by a further 6\%. 12 Find the final price after applying both the discount and the mark up: a A backpack originally priced at \$90 is marked up by 40\%. A few months later, the backpack is discounted from its new price by 10\%.

b

A washing machine originally priced at \$80 is discounted by 15\%. A few months later, the washing machine is marked up from its new price by 45\%. 13 The Run4Fun charity race is increasing in popularity. A year ago 60\,000 people registered to run, and this number is expected to increase by 6\% this year and then by another 8\% next year. How many people are expected to run next year? 14 A skipping rope priced at \$10 is marked up by 40\% and then later discounted by 40\%.

a

Calculate the new price of the skipping rope.

b

Explain why the new price of the skipping rope is not equal to the original price of the skipping rope.

15

An artist paints 1 landscape and 1 portrait painting, pricing them both at \$3200. • The price of the landscape painting is marked up once by 8\% and later marked up by a further 23\%. • The price of the portrait painting is marked up once by 23\% and later marked up by a further 8\%. a Find the final price of the landscape painting after applying both mark ups. b Find the final price of the portrait painting after applying both mark ups. c The artist notices that, after calculating all the mark ups, the price of the landscape and portrait paintings are equal. Explain why the prices are equal. 16 A television and a barbeque are both priced at \$3100.

• The price of the television is discounted once by 21\% and later discounted by a further 12\%.

• The price of the barbeque is discounted once by 12\% and later discounted by a further 21\%.

Will the final price of both items be equal? Explain your answer.

17

A stool priced at \$60 is marked up by 30\% and then marked up again by 70\%. Instead of calculating 2 separate mark ups, Judy claims that she can calculate the final price in a single step using the expression 60 \times 130\% \times 170\%. a Is Judy correct? Explain your answer. b Find the final price of the flute. 18 A flute priced at \$600 is marked up by 10\% and then marked up again by 40\%.

Instead of calculating 2 separate mark ups, Elizabeth claims that she can calculate the final price in a single step using the expression 600 \times 150\%, because 10 + 40 = 50.

a

b

Find the final price of the flute.

19

A tent priced at \$120 is discounted by 25\% and then discounted again by 15\%. Instead of calculating 2 separate discounts, Edward claims that he can calculate the final price in a single step using the expression 120 \times 75\% \times 85\%. a Is Edward correct? Explain your answer. b Find the final price of the tent. 20 A bookcase priced at \$110 is discounted by 20\% and then discounted again by 15\%. Instead of calculating 2 separate discounts, Carl claims that he can calculate the final price in a single step using the expression 110 \times 65\%, because 100 - 20 - 15 = 65.

a

b

Find the final price of the bookcase.

21

A book set priced at \$75 is discounted by 20\% and later marked up by 12\%. Instead of calculating 1 discount and 1 mark up, Luigi claims that he can calculate the final price in a single step using the expression 75 \times 80\% \times 112\%. a Is Luigi correct? Explain your answer. b Find the final price of the book set. 22 A computer game priced at \$80 is discounted by 15\% and later marked up by 20\%. Instead of calculating 1 discount and 1 mark up, Tom claims that he can calculate the final price in a single step using the expression 80 \times 105\%, because 100 - 15 + 20 = 105.

a

b

Find the final price of the computer game.

23

The price of a heater selling for \$234 is initially discounted by 14\% and later marked up by 14\%. Find the final sale price of the heater. 24 A jeweller began her career selling her necklaces for \$1500. After a few months she marked up the price by 16\%. A few weeks after that a video of her making the necklaces went viral, and she marked up the price by 11\%. In a few days she is due to appear on a popular podcast, and in anticipation of the increased demand she marks up the price by 13\%. Find the price of the jeweller's necklaces after all the mark ups.

25

In order to keep up with competition, a local shoemaker is forced to discount the price of his signature boots by 23\%. Noticing that he still isn't selling enough, the shoemaker discounts his boots by a further 22\% the next week, and then another 35\% the week after that. The boots were originally priced at \$110. Find the final price of the shoemaker's boots after all the discounts. 26 In response to the changing economy, the price of a car is marked up by 35\%, then discounted by 13\%, marked up again by 28\% and then finally discounted again by 14\%. If the car was originally priced at \$33\,000, find the new price of the car.