Ratio of a Quantity

Ratio of a Quantity

GCSE(F),

To distribute a quantity according to a ratio, carry out the following steps:

• Work out the total number of parts in the ratio;

• Divide the quantity by the number of parts;

• Multiply the totals for each ratio.

Share £50 in the ratio 2:3. The total number of parts is 2 + 3 = 5.

Work out the unit cost for each part: £50 ÷ 5 = £10.

Multiply each ratio by the unit amount: 2 x £10 = £20, and 3 x £10 = £30.

The share is therefore in the amounts £20 and £30.

Examples

1. There are 48 cars in a car park. If the ratio of red cars to other cars is 3 : 5, how many red cars were there?

Answer: 18

There are 3 + 5 = 8 parts altogether.

Number of cars in each part = 48 ÷ 8 = 6

Number of red cars = number of red parts x cars in each part

red cars = 3 x 6 = 18

2. Cement is being mixed with sand to make concrete in the ratio 1:5. If a total of 150kg of concrete is required, how much cement and sand is needed?

Answer: Cement: 25kg; Sand 125kg

The ratio is 1:5. Add the parts together 1 + 5 = 6 parts altogether.

Divide 150kg by 6 for 25kg per part.

Cement is 1 x 25 = 25, and sand = 5 x 25 = 125.

Check by adding together: 25 + 125 = 150.