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Unit A3 Section 4
Proportional Division

Sometimes a quantity has to be divided in a certain ratio. For example, two waiters may divide their tips in the ratio 2 : 3 because one has worked longer than the other. If they had a total of £5 in tips, one would get £2 and the other £3. If they had £20 in tips, one would get £8 and the other £12 .

Worked Examples

1

Mary and Nikki earn £285 by making curtains. Because Mary did more of the work they decide to divide the £285 in the ratio 3 : 2. How much do they earn each?

This problem is solved by dividing the £285 into 5 parts and giving 3 parts to Mary and 2 parts to Nikki. It is divided into 5 parts because the ratio is 3 : 2.

= £57

Mary's share = 3 × £57
= £171
Nikki's share = 2 × £57
= £114
2

Pineapple, orange and apple juices are mixed in the ratio 2 : 3 : 5 to make a new drink. Find the volume of each type of juice contained in 250 cm3 of the new drink.

Adding the terms of the ratio gives

2 + 3 + 5 = 10

So the volume of the drink must be divided into 10 parts.

= 25 cm3

Now the volume of each type of juice can be calculated.

Volume of pineapple juice = 2 × 25
= 50 cm3
Volume of orange juice = 3 × 25
= 75 cm3
Volume of apple juice = 5 × 25
= 125 cm3

Exercises

The ratio of the volume of oxygen to nitrogen in the air is 1 : 4. Find the volume of oxygen and the volume of nitrogen in 10 litres of air.

oxygen: l

nitrogen: l

The ratio of boys to girls in a school choir is 2 : 5. Find the numbers of boys and girls in the choir if there are 63 students in total.

boys, girls

Ben and Cheryl are given 140 stickers. They share them out in the ratio 4 : 3. How many stickers do they get each?

Ben:

Cheryl:

Andrea and Laura work as waitresses. Each week, Andrea works on 5 evenings and Laura on 4 evenings. They share any tips in the ratio 5 : 4 at the end of each week. How much do they get each if the total of tips for the week is:

(Give the answer to the nearest p.)

(a)

£12.69,

Andrea: £

Laura: £

(b)

£33.57,

Andrea: £

Laura: £

(c)

£24.00?

Andrea: £

Laura: £

Apples, bananas and oranges are mixed in the ratio 5 : 6 : 4 respectively by weight, to make a fruit salad. What weight of each type of fruit would be needed to make 6 kg of fruit salad?

apples: kg

bananas: kg

oranges: kg

A shoe shop sells a total of 240 pairs of shoes and sandals in one week. The ratio of sandals to shoes is 1 : 2. For the shoes, the ratio of high-heeled to flat is 7 : 1. For sandals, the ratio of flat to high-heeled is 1 : 3. Find the total number of flat shoes sold.

A fruit corner yogurt weighs 175 g altogether.

The ratio of the weight of fruit to the weight of yogurt is 2 : 5.

Calculate the weight of the fruit.

g