Proportion Worksheet with Answers

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GCSE · Ratio, Proportion and Rates of Change

3.6 Proportion

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

A shop sells notebooks in packs.
Pack A: 4 notebooks for GBP 3.20
Pack B: 6 notebooks for GBP 4.50

(a)Work out the cost of one notebook from Pack A.(1)

(b)Work out the cost of one notebook from Pack B.(1)

(c)State which pack is better value for money. Give a reason for your answer.(1)

(Total for Question 1 is 3 marks)

2

A recipe for a fruit crumble that serves 4 people uses:
300 g of apples
120 g of flour
80 g of butter
60 g of sugar

Aisha wants to make the crumble for 8 people.

(a)Work out the mass of apples needed for 8 people.(1)

(b)Work out the mass of flour needed for 8 people.(1)

(c)Work out the total mass of the crumble mixture (apples, flour, butter and sugar) needed for 8 people. Give your answer in kilograms.(1)

(Total for Question 2 is 3 marks)

3

The table shows the cost of buying ribbon. The cost is in direct proportion to the length.

Length (m)	Cost (GBP)
2	3.00
5	?
8	?

(a)Work out the cost of 5 m of ribbon.(1)

(b)Work out the cost of 8 m of ribbon.(1)

(Total for Question 3 is 2 marks)

4

Which of these graphs could show two quantities that are in direct proportion?

A) A straight line through the origin
B) A straight line that does not pass through the origin
C) A curve that passes through the origin
D) A horizontal line

(Total for Question 4 is 1 mark)

5

A supermarket sells bags of rice:
Small bag: 500 g for GBP 1.20
Medium bag: 800 g for GBP 1.84
Large bag: 1.5 kg for GBP 3.30

Work out which bag gives the best value for money.
You must show your working.

(Total for Question 5 is 4 marks)

6

The exchange rate is GBP 1 = $1.28

(a)Convert GBP 250 to dollars.(2)

(b)Convert $60 to pounds. Give your answer to the nearest penny.(2)

(Total for Question 6 is 4 marks)

7

A recipe for pancake batter serves 5 people and uses 250 g of flour and 2 eggs.
Ben wants to make enough batter for 8 people.

(a)Work out how much flour Ben needs for 8 people.(2)

(b)Work out the least number of whole eggs Ben needs for 8 people. Give a reason for rounding as you did.(2)

(Total for Question 7 is 4 marks)

8

1 tin of paint covers 12 m² of wall.
Priya needs to paint a wall with area 30 m².
Paint is only sold in whole tins.
Work out the least number of tins Priya needs to buy.

(Total for Question 8 is 3 marks)

9

Chloe is paid at a rate that is directly proportional to the number of hours she works.
She is paid GBP 38.25 for 5 hours of work.

(a)Work out how much Chloe is paid for 8 hours of work.(2)

(b)One week Chloe is paid GBP 68.85. Work out how many hours she worked.(2)

(Total for Question 9 is 4 marks)

10

A car uses 6 litres of petrol to travel 84 km.
Assume the amount of petrol used is directly proportional to the distance travelled.

(a)Work out the distance that can be travelled using 20 litres of petrol.(2)

(b)Work out how much petrol is needed to travel 175 km.(2)

(Total for Question 10 is 4 marks)

11

A map has a scale of 1 : 25000.

(a)The distance between two villages on the map is 6.4 cm. Work out the real distance between the villages, in kilometres.(2)

(b)The real distance between two towns is 12 km. Work out the distance between the towns on the map, in centimetres.(2)

(Total for Question 11 is 4 marks)

12

While on holiday in the USA, Tom sees a jacket priced at $84.
The exchange rate is GBP 1 = $1.40.
In the UK, the same jacket costs GBP 54.
Work out the difference in price, in pounds, between buying the jacket in the USA and in the UK.

(Total for Question 12 is 3 marks)

13

A recipe for lemonade that makes 6 glasses needs 3 lemons and 250 ml of water.
Nadia has 8 lemons and 900 ml of water.
Work out the greatest number of glasses of lemonade Nadia can make, assuming she can only make whole batches of the recipe.

(Total for Question 13 is 4 marks)

14

The cost of hiring a bouncy castle for a party is directly proportional to the number of hours it is hired for.
It costs GBP 45 to hire for 3 hours.

(a)Work out the cost of hiring the bouncy castle for 7 hours.(2)

(b)Sam has a budget of GBP 100. Work out the maximum whole number of hours he can hire the bouncy castle for.(2)

(Total for Question 14 is 4 marks)

15

To make a shade of green paint, blue paint and yellow paint are mixed in direct proportion.
80 ml of blue paint is mixed with 120 ml of yellow paint to make one batch of the shade.

(a)Bilal has 200 ml of blue paint. Work out how much yellow paint he needs to make the same shade, using all the blue paint.(2)

(b)Bilal has an unlimited supply of blue paint but only 300 ml of yellow paint. Work out the maximum total amount of the green paint mixture he can make.(2)

(Total for Question 15 is 4 marks)

16

A hosepipe fills a paddling pool at a constant rate. It takes 15 minutes to fill the pool with 180 litres of water.

(a)Work out how many litres of water flow through the hosepipe in 1 minute.(1)

(b)Work out how long it will take to fill a larger pool that holds 310 litres. Give your answer in minutes and seconds.(3)

(Total for Question 16 is 4 marks)

17

The number of pages printed by a printer is directly proportional to the amount of ink used.
The printer uses 24 ml of ink to print 400 pages.

(a)Work out how many pages can be printed using 60 ml of ink.(2)

(b)Work out how much ink, in ml, is needed to print 1500 pages.(2)

(Total for Question 17 is 4 marks)

18

It takes 6 builders 15 days to build a wall.
Assume all builders work at the same constant rate, and the time taken is inversely proportional to the number of builders.

(a)Work out how many days it would take 9 builders to build the same wall.(3)

(b)The wall needs to be completed in 5 days. Work out the minimum number of builders needed.(2)

(Total for Question 18 is 5 marks)

19

y is directly proportional to x.
When x = 5, y = 40.

(a)Find a formula for y in terms of x.(2)

(b)Work out the value of y when x = 12.(1)

(c)Work out the value of x when y = 100.(2)

(Total for Question 19 is 5 marks)

20

The cost of catering for a conference is directly proportional to both the number of delegates and the number of days.
Catering for 40 delegates for 3 days costs GBP 2160.

(a)Work out the cost of catering for 40 delegates for 5 days.(2)

(b)Work out the cost of catering for 75 delegates for 3 days.(2)

(c)A different conference has a catering budget of GBP 3600 for 60 delegates. Work out the maximum whole number of days the catering budget will allow.(3)

(Total for Question 20 is 7 marks)

Mark scheme · 3.6 Proportion

Question 1

(a) B1 0.80 (GBP) oe cao
(a) Answer: GBP 0.80
(b) B1 0.75 (GBP) oe cao
(b) Answer: GBP 0.75
(c) B1 Pack B, with correct comparison of unit costs (75p is less than 80p) ft from (a) and (b)
(c) Answer: Pack B, because 75p per notebook is cheaper than 80p per notebook

Question 2

(a) B1 600 (g) cao
(a) Answer: 600 g
(b) B1 240 (g) cao
(b) Answer: 240 g
(c) B1 1.12 (kg) oe (1120 g) ft
(c) Answer: 1.12 kg

Question 3

(a) B1 7.50 cao
(a) Answer: GBP 7.50
(b) B1 12.00 cao ft
(b) Answer: GBP 12.00

Question 4

B1 A
Answer: A

Question 5

M1 small bag: (1.20 / 500) x 100 = 24 (pence per 100 g) oe
M1 medium bag: (1.84 / 800) x 100 = 23 (pence per 100 g) oe
M1 large bag: (3.30 / 1500) x 100 = 22 (pence per 100 g) oe
A1 large bag (cao), dep on at least two correct unit costs shown
Answer: Large bag (22p per 100 g, compared with 23p for medium and 24p for small)

Question 6

(a) M1 250 x 1.28
(a) A1 320 cao
(a) Answer: $320
(b) M1 60 / 1.28
(b) A1 46.88 awrt
(b) Answer: GBP 46.88

Question 7

(a) M1 250 / 5 (= 50) or 250 x 8/5
(a) A1 400 (g) cao
(a) Answer: 400 g
(b) M1 (2/5) x 8 (= 3.2) oe
(b) A1 4 (eggs), with reason that eggs cannot be used in a fraction so must round up cao
(b) Answer: 4 eggs

Question 8

M1 30 / 12 (= 2.5)
M1 rounding up to the next whole number of tins (dep)
A1 3 cao
Answer: 3 tins

Question 9

(a) M1 38.25 / 5 (= 7.65) or 38.25 x 8/5
(a) A1 61.20 cao
(a) Answer: GBP 61.20
(b) M1 68.85 / 7.65
(b) A1 9 cao
(b) Answer: 9 hours

Question 10

(a) M1 84 / 6 (= 14) oe
(a) A1 280 (km) cao
(a) Answer: 280 km
(b) M1 175 / 14
(b) A1 12.5 (litres) cao
(b) Answer: 12.5 litres

Question 11

(a) M1 6.4 x 25000 (= 160000 cm) oe or 6.4 x 0.25
(a) A1 1.6 (km) cao
(a) Answer: 1.6 km
(b) M1 12 / 0.25 oe
(b) A1 48 (cm) cao
(b) Answer: 48 cm

Question 12

M1 84 / 1.40
A1 60 (GBP) oe
B1 6 (GBP), cheaper in the UK, dep on correct 60 (ft)
Answer: GBP 6 cheaper in the UK

Question 13

M1 8 / 3 (= 2.67...) oe
M1 900 / 250 (= 3.6) oe
A1 2 (recipes), identifying lemons as the limiting ingredient
A1 12 (glasses) cao dep
Answer: 12 glasses

Question 14

(a) M1 45 / 3 (= 15) oe
(a) A1 105 (GBP) cao
(a) Answer: GBP 105
(b) M1 100 / 15 (= 6.67) oe
(b) A1 6 cao, with rounding down reasoning
(b) Answer: 6 hours

Question 15

(a) M1 200 x (120/80) oe
(a) A1 300 (ml) cao
(a) Answer: 300 ml
(b) M1 300 x (80/120) (= 200) oe
(b) A1 500 (ml) cao
(b) Answer: 500 ml

Question 16

(a) B1 12 (litres per minute) cao
(a) Answer: 12 litres per minute
(b) M1 310 / 12 (= 25.83...) oe
(b) M1 0.8333... x 60 (= 50) (dep)
(b) A1 25 minutes 50 seconds cao
(b) Answer: 25 minutes 50 seconds

Question 17

(a) M1 60 x (400/24) oe
(a) A1 1000 (pages) cao
(a) Answer: 1000 pages
(b) M1 1500 x (24/400) oe
(b) A1 90 (ml) cao
(b) Answer: 90 ml

Question 18

(a) M1 6 x 15 (= 90) oe
(a) M1 90 / 9 (dep)
(a) A1 10 (days) cao
(a) Answer: 10 days
(b) M1 90 / 5 ft
(b) A1 18 (builders) cao
(b) Answer: 18 builders

Question 19

(a) M1 y = kx and 40 = 5k, so k = 8 oe
(a) A1 y = 8x oe
(a) Answer: y = 8x
(b) B1 96 cao ft from (a)
(b) Answer: y = 96
(c) M1 100 / 8 ft
(c) A1 12.5 cao
(c) Answer: x = 12.5

Question 20

(a) M1 2160 x (5/3) oe or 40 x 5 x 18
(a) A1 3600 (GBP) cao
(a) Answer: GBP 3600
(b) M1 2160 x (75/40) oe or 75 x 3 x 18
(b) A1 4050 (GBP) cao
(b) Answer: GBP 4050
(c) M1 60 x 18 (= 1080) oe (daily cost for 60 delegates)
(c) M1 3600 / 1080 (= 3.33...) dep
(c) A1 3 (days) cao, with rounding down reasoning
(c) Answer: 3 days

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