Cambridge International Mathematics

Assumed Knowledge (Number) 17

3 A recipe for tomato soup uses tomatoes and onions in the ratio7:2.If 21 kg of tomatoes are used,

how many kilograms of onions are needed?

4 An orchard has apple trees and pear trees in the ratio5:3.

If there are 180 pear trees, how many apple trees are there?

5 A car cleaning service increases the cost of a$15‘standard

clean’ to$18. The$25‘deluxe clean’ is increased in the same

ratio as the ‘standard’. How much does a ‘deluxe clean’ cost

now?

6 Concrete is mixed in a ratio of premix to cement of6:1. If I have 540 kg of premix, how much

cement do I need?

7 The mass of two bags is in the ratio7:12. The bigger bag has a mass of 48 kg.

a Find the mass of the smaller bag. b Find the combined mass of the bags.

8aIncrease$12in the ratio: i 5:4 ii 2:1 iii 15 : 2

b Decrease 200 kg in the ratio: i 3:4 ii 4:5 iii 1:20

THE UNITARY METHOD FOR RATIOS

Some ratio problems are easily handled using theunitary method.

ConsiderExample 23where walkers : guides=27:x

i.e., 9 : 2 = 27 :x

The unitary method is: 9 parts is 27

) 1 part is 27 ¥9=3

) 2 parts is 3 £2=6

) 6 guides were needed.

Example 24 Self Tutor

The ratio of Pam’s height to Sam’s height is7:6. If Pam is 1 : 63 m tall, how tall is

Sam?

Let Sam’s height bexm.

Pam : Sam=7:6

) 1 :63 :x=7:6

So, 7 parts is 1 : 63 m

) 1 part is 1 : 63 ¥ 7 m

) 6 parts is 1 : 63 ¥ 7 £ 6 m

) Sam’s height is¼ 1 : 40 m.

or Let Sam’s height bexm.

Pam : Sam=7:6

) 1 :63 :x=7:6

)

x

1 : 63

=

6

7

) x=^67 £ 1 : 63

) x¼ 1 : 40

) Sam’s height is¼ 1 : 40 m.

The unitary

method works

well with harder

ratio problems.

IGCSE01

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