Middle Years

# 4.03 Percentage of a quantity

Worksheet
Percentage of a quantity without a calculator
1

Evaluate the following to the nearest 5 cents:

a
10\% of \$16.20 b 10\% of \$696.60
c
10\% of \$955.97 d 5\% of \$41.70
e
5\% of \$319.80 f 5\% of \$466.11
g
1\% of \$66.20 h 1\% of \$14.37
i
1\% of \$888.60 j 15\% of \$86
2

Evaluate the following:

a
10\% of 5607
b
25\% of 2900
c
50\% of 1800
d
28\% of 5000
e
25\% of 7900 grams
f
30\% of 7 metres
3

Consider the following quantities:

• 55\% of 10 metres

• 55\% of 1 metre

• 5\% of 100 metres

• 50\% of 10 metres

State the largest quantity.

4

Answer the following questions in order to find 45\% of 5 hours without a calculator.

a

How many minutes are there in 5 hours?

b

Find 10\% of 300 minutes.

c

Find 5\% of 300 minutes.

d

Hence, find 45\% of 300 minutes.

5

What percentage of the squares are shaded?

6

Use rounding to approximate 7.8\% of \$89\,099.99. Percentage of a quantity with a calculator 7 Evaluate the following to the nearest 5 cents: a 10\% of \$321.06

b

26\% of \$126.60 8 Evaluate the following to two decimal places, if necessary: a 51.3\% of 240 b 59\% of 440 kilometres c 5.2\% of 80 kilograms d 900\% of 90 metres e 14\% of 100 grams f 74\% of 4600 kilometres g 16\% of 4590 \text{ kg} h 2\dfrac{1}{4}\% of 8500 9 Evaluate the following in metres: a 25\% of 2 kilometres b 12.5\% of 2 kilometres c 37.5\% of 2 kilometres 10 Evaluate the following quantities as improper fractions: a 24\% of 272 b 51\% of 169 11 Evaluate 61\% of 496, as a mixed number. Applications 12 A salesperson earns a 13\% commission on their total sales each week. In one week, their sales amounted to \$640.

a

Find 10\% of their total sales.

b

Find 3\% of their total sales, correct to two decimal places.

c

Hence, find the total commission they made that week, correct to two decimal places.

13

A telephone marketer earns a 13\% commission on their total sales each week. In one week, their sales amounted to \$970. a Find 10\% of their total sales. b Find 3\% of their total sales, correct to two decimal places. c Hence, find the total commission they made this week, correct to two decimal places. 14 A car manufacturer estimated that 17\% of 2700 cars produced are faulty. The steps to find 17\% of 2700 cars are given in random order. When put in the correct order, which step should come second? A \dfrac{45\,900}{100} B 17\% \times 2700 C 459 D \dfrac{17}{100} \times 2700 15 Lisa scored 70\% on her Maths exam, which was marked out of 140. What was Lisa's actual mark out of 140? 16 Jay scored 92\% of a possible 600 marks. He had aimed to score 96\% of the marks. How many more marks were required to reach his goal? 17 Valentina has completed 25\% of the necessary 70 hours of pilot training. a Find 25\% of 70 hours, correct to one decimal place. b Find 2.5\% of 70 hours, correct to two decimal places. c Quentin has completed 27.5\% hours of the necessary training. Find how many hours he has completed, correct to two decimal places. 18 Liam works 0.8 days for every day of the five day work week. a What percentage of the work week does Liam work? b What percentage of the five day week does Liam not work? c What percentage of the whole 7 day week does he work? Express your answer as a percentage correct to one decimal place. 19 Ben is going to purchase some sports gear on layby. This involves paying some money as a deposit, and paying the remainder later. The price of the gear is \$65.

a

If he needs to pay 25\% deposit, how much is this?

b

Calculate the remaining balance on the layby purchase.

20

When tickets to a football match went on sale, 29\% of the tickets were purchased in the first hour.

a

If the stadium seats 58\,000 people, find the number of seats still available after the first hour.

b

If the stadium seats 60\,000 people, find the number of seats still available after the first hour.

21

A theatre has a capacity of 1000 people. On opening night the theatre was 95\% full. On the second night it was 70\% full. Find the total number of people that attended the theatre on the first two nights.

22

In a recent survey of planes landing at a major airport, it was observed that 19\% of the flights were delayed less than an hour and 3\% of the flights were delayed an hour or more but less than two hours.

a

Find the percentage of flights that are delayed less than two hours.

b

If 9000 flights arrive at the airport in a day, how many flights are delayed less than two hours?

23

A frozen apple pie weighing 331 grams is advertised as being 90\% fat free. How many grams of fat are there in the pie? Round your answer to one decimal place.

24

Valentina heated 500 \text{ mL} of solution. After a few minutes, 25\% of the solution had evaporated. Find the quantity of the solution that remained.

25

Ellie bought a 454 \text{ mL} drink that claimed to be orange juice. In the ingredients list it said that orange juice made up 17\% of the drink. To estimate the amount of orange juice in the drink, which of the following quantities would give the closest answer:

A
10\% \times 454
B
20\% \times 454
C
10\% \times 400
26

Inflation between the years 2009 and 2010 was 1.7\%, such that a purchase made in 2009 for \$100 would be worth \$101.70 in 2010. A product was valued at \$3200 in 2009. a Find 1\% of the product's value. b Find 7\% of the product's value. c Find 0.7\% of \$3200.

d

What is 1.7\% worth?

e

Find the value of the product in 2010.