10.4 Solving ratio problems where only the difference in amounts is given
Earlier in the section you came across the question below. Let’s have a look at how we could solve this.
Example: Solving ratio amounts from the difference
Ishmal and Ailia have shared some money in the ratio 3:7.
Ailia receives £20 more than Ishmal. How much does Ishmal receive?
You know that the difference between the amount received by Ishmal and the amount received by Ailia is £20. You can also see that Ailia gets 7 parts of the money whereas Ishmal only gets 3.
The difference in parts is therefore 7 − 3 = 4. So 4 parts = £20.
Now this is established, you can work out the value of one part by doing:
£20 ÷ 4 = £5
As you want to know how much Ishmal received you now do:
£5 × 3 = £15
As an extra check, you can work out Ailia’s by doing:
£5 × 7 = £35
This is indeed £20 more than Ishmal.
Activity 27: Ratio problems where difference given
Now try solving this type of problem for yourself.
The ratio of female to male engineers in a company is 2:9. At the same company, there are 42 more male engineers than females.
How many females work for this company?
A garden patio uses grey and white slabs in the ratio 3:5. You order 30 fewer grey slabs than white slabs.
How many slabs did you order in total?
The difference in parts between males and females is 9 − 2 = 7 parts.
You know that these 7 parts = 42 people.
To find 1 part you do:
42 ÷ 7 = 6
Now you know that 1 part is worth 6 people, you can find the number of females by doing
6 × 2 = 12 females
- The number of males is 6 × 9 = 54.
The difference between 54 and 12 is 42.
The difference in parts between grey and white is 5 − 3 = 2 parts.
These 2 parts are worth 30. To find 1 part you do:
- 30 ÷ 2 = 15
To find grey slabs do:
- 15 × 3 = 45
To find white slabs do:
- 15 × 5 = 75
The difference between the number of grey and white slabs is 30 (75 − 45).
Now you know both grey and white totals, you can find the total number of slabs by doing:
- 45 + 75 = 120 slabs in total.
Even though there are different ways of asking ratio questions, the aim of any ratio question is to determine the value of one part. Once you know this, the answer is simple to find!
Ratio can also be used in less obvious ways. Imagine you are baking a batch of scones and the recipe makes 12 scones. However, you need to make 18 scones rather than 12. How do you work out how much of each ingredient you need? The final ratio section deals with other applications of ratio.