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1.04 Finding the total amount

Worksheet
Unitary method
1

For each of the following:

i

Find 1\% of the quantity.

ii

Find the total quantity.

a
11\% of a quantity is 22.
b
40\% of a quantity is 960.
c
25\% of a quantity is 150\text{ m}.
d
35\% of a quantity is 770\text{ km}.
2

Find the original number if:

a
1\% of the number is 20.
b
2\% of the number is 8.
c
10\% of the number is 5.
d
10\% of the number is 19.
e
20\% of the number is 10.
f
25\% of the number is 12.
g
50\% of the number is 14.
h
200\% of the number is 18.
i
150\% of the number is 3.
3

If 36\% of a quantity is equal to 2412:

a

Find 1\% of the quantity.

b

Find 83\% of the quantity.

4

7\% of a price is \$49.

a

Find 1\% of the price.

b

Find 30\% of the price.

5

If 21\% of a quantity is equal to 378\text{ mL}:

a

Find 1\% of the quantity.

b

Find 71\% of the quantity.

6

Find the original number (to the nearest whole number) if:

a
150\% of the number is 285.
b
420\% of the number is 850.
c
360\% of the number is 9100.
Applications
7

The 64 girls at Victoria's party represent 80\% of all the guests. Find the total number of guests at the party.

8

A city has a yearly water supply of 27\,000\,000 megalitres. It gets 14\% of this water supply from melted snow. Find the amount of water that comes from melted snow each year.

9

A total of 36\,000 engineers were hired last year. This represents 9\% of the total number of engineers employed in the country. How many engineers are employed in the country altogether?

10

Every item in a store is sold at 10\% more than its cost. If a product is sold for \$220, find:

a

The cost price

b
The profit
11

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

a

1\% of her weekly sales.

b

The total value of her weekly sales.

12

An investor sold his portfolio at 8\% profit for a price of \$2000. Calculate the original value of his portfolio.

13

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.

14

When a rock sample was examined, it was found that 4.1 kilograms of it was copper.

If this sample represents 10\% of the total copper in the rock bed, how many kilograms of copper were there in the rock bed?

15

33\dfrac{1}{3}\% of a quantity is 448 grams. Find 66\dfrac{2}{3}\% of the same quantity.

16

Beth spends 90\% of her weekly income on rent. If her rent is \$720 each week, find her weekly income.

17

462 students represent 30\% of the school population. Find the number of students that make up 60\% of the school population.

18

A store is having a 15\% off sale. Calculate the original price of a discounted item that is on sale for \$3723.75.

19

Iain spent some time volunteering in a community. He spent 10\% of his time volunteering at schools and 2\% of his time volunteering at the local hospital. The remaining 132 days he spent volunteering at animal shelters.

How many days did Iain volunteer at the local hospital?

20

Gwen has \$200 to spend on a new laptop. The sale price of the laptop includes the original price plus a sales tax of 9\%. Find the greatest original price of the laptop that Gwen can afford. Round your answer to the nearest dollar.

21

Fred’s new cable television bill is \$98 per month. This is 140\% of his monthly bill from last year, when he had the basic cable package. What was his monthly cable television bill last year?

22

A manufacturer is selling its old machinery for \$34\,320, which represents a loss of 12\%. At what price did the manufacturer originally purchase the machinery?

23

James bought a unique number plate and sold it to a car owner at 17\% profit, who then sold it to an interstate buyer at 2\% profit. If the interstate buyer bought it for \$6500, what did James originally pay for the number plate?

Algebraic applications
24

After a 5\% sales tax is added, the price of a trampoline is \$367.50. Let p represent the original price of the trampoline, before tax is added.

a

Write an algebraic expression in terms of p for the amount of tax added.

b

Hence, determine the price of the trampoline before tax.

25

Peter and Luigi are building a new supercomputer that will cost them \$195\,300. This price is 2\% higher than the price they originally budgeted for. Let b represent the original price that they budgeted for.

a

Write an algebraic expression in terms of b for the increase in cost.

b

Hence, determine the price of the supercomputer that Peter and Luigi originally budgeted for.

26

After a 40\% reduction, the price of a motor scooter is \$240. Let p represent the original price of the motor scooter.

a

Write an algebraic expression in terms of p for the amount that the price was reduced by.

b

Hence, determine the original price of the motor scooter.

Multiple percentage changes
27

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

Find the original selling price of the dress.

28

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 stock. Round your answer to the nearest dollar.

29

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.

30

A kitchen appliance is selling for \$1136.64 after a mark-up of 28\% and 11\% GST 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.

31

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

a

20\%

b

20\% and 16\% successively

32

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.

33

The price of a iPad is reduced by 30\%, and then later reduced by a further 25\%. The new price of the iPad is \$890.

Determine the original price of the iPad to the nearest dollar.

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Outcomes

1.1.1.6

apply percentage increase or decrease in various contexts, e.g. determining the impact of inflation on costs and wages over time, calculating percentage mark-ups and discounts, calculating GST, calculating profit or loss in absolute and percentage terms, and calculating simple and compound interest

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