Sharing in a given ratio
A ratio can also be used to share a quantity into parts.
Example 1
Rebeckah and Amy share £280 in the ratio 5:2. How much money will they each receive?
1. Add up the ratio to find the total number of parts:
5 + 2 = 7 parts
2. Divide the total amount by the number of parts:
£280 ÷ 7 = £40
Each part is worth £40
3. Multiply by the ratio to find each person’s share:
5 × £40 = £200 (Rebeckah’s share)
2 × £40 = £80 (Amy’s share)
4. Check these add up to the original amount:
£200 + £80 = £280
Example 2
David and Paul share the cost of a football season ticket in the ratio 3:7. If David pays £105, how much does the season ticket cost in full?
- David pays three parts = £105: £105 ÷ 3 = £35 = 1 part
- The cost had been split into 3 + 7 = 10 parts
- £35 × 10 = £350
The total cost of the ticket is £350.
Question
An alloy consists of magnesium, zinc and copper in the ratio 5:3:4. If an alloy compound weighs 720 g, how much of this would be magnesium, zinc and copper?
1. Add the total number of parts:
5 + 3 + 4 = 12 parts
2. Find out how much one part is:
720 g ÷ 12 = 60 g
3. Multiply each ratio by 60:
60 g × 5 = 300 g of magnesium
60 g × 3 = 180 g of zinc
60 g × 4 = 240 g of copper
4. Check they add up to 720 g:
300 + 180 + 240 = 720 g
Question
To make pink paint I mix red and white paint in the ratio 4:5. If I use 600 ml of red paint, how many litres of paint will I make?
- Red paint = 4 parts = 600 ml
- 600 ml ÷ 4 = 150 ml = One part
- Total parts = 4 + 5 = 9
- 150 ml × 9 = 1,350 ml of paint
- Convert to litres by ÷ 1,000: 1,350 ÷ 1,000 = 1.35 litres of paint made
