Cambridge International Mathematics

Assumed Knowledge (Number) 19

6 The map alongside has a scale of1 : 500 000, which

means that 1 cm on the map represents500 000cm in

real life.

a If the distance BC=2: 1 cm on the map, find

the actual distance between B and C.

b If E and C are 13 : 5 km apart, find the length of

EC on the map.

7

8 A quantity is increased in the ratio 5:4, and then decreased in the ratio 3:4. Find, in simplest

form, the ratio of the final quantity to the original quantity.

USING RATIOS TO DIVIDE QUANTITIES

Quantities can be divided in a particular ratio by considering thenumber of partsthe whole is divided into.

Example 27 Self Tutor

An inheritance of$60 000is to be divided between Donny and Marie

in the ratio2:3. How much does each receive?

There are 2+3=5 parts.

) Donny gets^25 of$60 000

=^25 £60 000

= $24 000

and Marie gets^35 of$60 000

=^35 £60 000

= $36 000

1 What is the total number of parts represented by the following ratios?

a 2:3 b 4:1 c 7:9 d 12 : 5

e 10 : 3 f 3:16 g 7:4 h 9:10

2 Divide a 50 cm piece of string in the following ratios:

a 1:1 b 4:1 c 3:2 d 7:13

3 Divide:

a $50in the ratio 1:4 b E 35 in the ratio 3:4 c 90 kg in the ratio 4:5

4 Lottery winnings of$400 000are to be divided in the ratio5:3. Find the larger share.

5 The ratio of girls to boys in a school is 5:4. If there are 918 students at the school, how many are

girls?

6 A man leaves200 000euros to his sons Aleksi and Kristo in the ratio of their ages when he dies. Aleksi

is 4 years older than Kristo. When the father dies, Aleksi is 62.

a How old is Kristo? b How much does Aleksi inherit (to the nearest euro)?

c How much does Kristo inherit (to the nearest euro)?

EXERCISE F.5

A bakery decides to donate cents to charity for

every loaf of bread bought. If the bakery sells

worth of bread, how much is donated to

charity?

5

$1 95

$3217 50

:

:

A

E

F

B

C

D

Scale: 1 : 500 000¡¡ ¡

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