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2.07 Repeated percentage change

Worksheet
Successive percentage change
1

A dining table selling for \$1000 is discounted at 5\% and then again at 6\%.

a

What is the price of the dining table after the first discount is applied?

b

What is the price of the dining table after the second discount is applied?

c

If the percentage discount is changed to a single percentage of 11\% by adding 5\%+6\% find the new discounted price.

d

Is the single discount of 11\% equal to successive discounts of 5\% and 6\%?

e

Find the single discount rate that is equivalent to successive discounts of 5\% and 6\%? Round your answer to one decimal place.

2

Shares which originally cost \$24 each, increase in value by 5\%, and then they increase again by 9\%.

a

What is the cost of the shares after the first increase?

b

What is the cost of the shares after the second increase?

c

By how much has the share price increased overall?

d

Find the single percentage increase rate that is equivalent to the successive increases. Round your answer to two decimal places.

3

Wally is a bricklayer and buys a set of tools that cost \$1100 but are on sale at 11\% off, and then an additional store wide sale discount of 12\% applies to the items as well. Wally then receives a further 9\% trade discount.

a

What is the cost of the set of tools after the first discount is applied?

b

What is the cost of the set of tools after the additional store wide sale discount is applied?

c

What is the final cost of the set to the bricklayer?

d

Find the single percentage discount rate that is equivalent to the successive discounts. Round your answer to two decimal places.

4

A set of professional knives for chefs originally cost \$1900 and is now on sale at 20\% off. A chef then receives a further 9\% trade discount on the reduced price.

a

What is the final cost of the set to a chef?

b

How much overall is saved in dollars?

c

Find the single percentage discount rate that is equivalent to the successive discounts. Round your answer to two decimal places.

5

A PC originally sells at \$4700.

a

Calculate its sales price after successive discounts of 6\% and 9\%.

b

Calculate its sales price after successive discounts of 9\% and 6\%.

c

Does the order of discounting affect the sales price?

d

Calculate its sales price after successive discounts of 8\%, 7\% and 5\%.

6

The price of a heater selling for \$234 is initially discounted by 14\% and later marked up by 14\%. What is the final sales price?

7

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?

8

A laptop is originally priced at \$700. Successive discounts of 12\% and 4\% are applied to the cost of the laptop.

a

Find the final price of the laptop.

b

Find the total discount received.

Overall percentage change
9

Quentin wants to buy a jacket that is originally priced at \$220 and is on sale at 14\% off. The jacket is then further discounted by 18\%.

a

Calculate the final selling price of the jacket.

b

What overall percentage discount is this equivalent to? Round your answer to two decimal places.

c

Quentin believes that if the discounts are applied in the reverse order (that is the 18\% discount first and then the 14\% discount) he will save more money. Is he correct?

10

A plumber buys bathroom fixtures for a job that cost \$1100 but are on sale at 15\% off. The plumber receives a further 13\% trade discount after the sale discount is taken off.

a

What is the final cost of the set to the plumber?

b

What overall percentage discount is this equivalent to? Round your answer to two decimal places.

c

The plumber was expecting to save \$308, explain what his misunderstanding could have been.

d

Explain the relationship between the discount received from applying successive percentage discounts and the discount received if the individual percentages were added.

11

Which offer gives the greater discount?

a

Offer 1: A single discount of 13\%

Offer 2: Successive discounts of 6\% and 11\%

b

Offer 1: A single discount of 16\%

Offer 2: Successive discounts of 5\% and 11\%

12

The price of a dress was reduced by 30\% and then again by 30\%.

a

After the first decrease, what percentage of the original price will the new price be?

b

After the second decrease, what percentage of the decreased price will the new price be?

c

What was the overall percentage decrease?

d

The overall percentage decrease when the price is reduced by 30\% twice is equal to 2 \times 30\%. True or false?

13

The price of a phone was increased by 40\% and then again by 40\%.

a

After the first increase, what percentage of the original price will the new price be?

b

After the second increase, what percentage of the increased price will the new price be?

c

What was the overall percentage increase?

d

The overall percentage increase when the price is increased by 40\% twice is equal to 2 \times 40\%. True or false?

14

For each of the following, determine the overall percentage decrease:

a

The price of a phone which was reduced by 25\% and then again by 25\%.

b

The price of a dress which was reduced by 63\% and then again by 63\%.

c

The price of a shirt which was reduced by 10\% and then increased by 10\%.

d

The price of a phone which was reduced by 75\% and then increased by 75\%.

e

The price of a shirt which was reduced by 46\% and then increased by 46\%.

f

The price of a dress which was increased by 20\% and then reduced by 20\%.

g

The price of a shirt which was increased by 50\% and then reduced by 50\%.

h

The price of a phone which was increased by 93\% and then reduced by 93\%.

15

For each of the following, determine the overall percentage increase:

a

The price of a phone which was increased by 75\% and then again by 75\%.

b

The price of a shirt which was increased by 97\% and then again by 97\%.

c

The price of a dress which was reduced by 20\% and then increased by 44\%.

d

The price of a dress which was increased by 19\% and then reduced by 14\%.

16

Rochelle is in charge of keeping everyone happy in her workplace, and seems to be doing a good job. The number of complaints submitted has decreased 6\% in the twelve months since she took over and she expects it to fall by another 10\% over the next year.

a

Express the amount of complaints submitted in the last twelve months as a percentage of the number of complaints submitted before she took over.

b

Express the amount of complaints she expects to see submitted in the next year as a percentage of the amount submitted in the previous twelve months.

c

Calculate the number of complaints expected over the next year as a percentage of the amount that were submitted before Rochelle took over.

d

Hence, find the total percentage decrease over the two years.

17

Maximilian is an American tourist having lunch in Sydney, and wants to leave a sizeable tip for his waiter. However, he also must pay the Goods & Services Tax (GST) on his meal.

a

If he wants to leave a 20\% tip and the GST is fixed at 10\%, express the total amount of money he will pay as a percentage of the pre-tax value of the meal.

b

What percentage have the GST and tip added to the amount paid for the meal?

18

A country's GDP (Gross Domestic Product) contracted by 4\% one year due to a drought, but then grew by 6\% the next year when the weather returned to normal.

a

Express the country's GDP during the drought as a percentage of the previous year's GDP.

b

Express the country's GDP in the year after the drought as a percentage of the drought affected GDP.

c

Calculate the new GDP as a percentage of the original.

d

Hence, find the percentage change over the two years.

e

Is this change an overall increase or decrease?

19

Bob has invested heavily in a certain company. One day it was reported that the company's factory was damaged by a fire and its share price fell by 40\%. However, when it was revealed the next day that the company had insurance and wouldn't be too badly affected, the shares recovered by 40\%.

a

Express the share price after the original announcement as a percentage of the previous day's price.

b

Express the share price after the insurance announcement as a percentage of the price after the original fire announcement.

c

Calculate the final share price as a percentage of the price before either announcement.

d

Hence, evaluate the percentage change over the two days.

e

Is this change an overall increase or decrease?

Find original amount
20

A dress is on sale for \$85.17 after a discount of 11\% and an additional discount of 13\%.

a

Complete the following statement:

\text{Sale price }= \text{ Original price } \times⬚ \times ⬚

b

Hence find the original selling price of the dress.

21

Shares in a company have a current value of \$82.84 after an initial increase of 9\% and then drop of 5\%.

a

Complete the following statement:

\text{Sale price }= \text{ Original price } \times⬚ \times ⬚
b

What overall percentage increase is this equivalent to?

c

Find the original selling price of the shares. Round your answer to the nearest dollar.

22

A guitar is on sale for \$403.69 after a discount of 21\% and an additional discount of 27\%.

a

Complete the following statement:

\text{Sale price }= \text{ Original price } \times⬚ \times ⬚
b

What overall percentage change is this equivalent to?

c

Find the original selling price of the guitar. Round your answer to the nearest dollar.

23

A kitchen appliance is selling for \$1136.64 after a mark-up of 28\% and then GST (11\%) was added to the price.

a

What overall percentage increase is this equivalent to?

b

What was the cost price of the item? Round your answer to the nearest dollar.

24

After discounting, a clothes dryer sold for \$855. Calculate the original price if the discount was:

a

20\%

b

20\% and 16\% successively

25

The population of a town is 64\,609 after two years of increasing at 2\% per year. Find the population of the town two years ago. Round up to the nearest person.

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Outcomes

1.1.3.5

determine the overall change in a quantity following repeated percentage changes [complex]

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