7.3 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.
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 15: Ratio problems where difference given
Now try solving this type of problem for yourself.
The ratio of female to male patients attending a clinic is 2:9. There 42 more male patients than females.
How many females attending the clinic?
You need to order large and small gauze dressings in the ratio 3:5. You order 30 fewer large dressings than small dressing.
How many dressings 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 difference in parts between small and large is 5 − 3 = 2 parts. These 2 parts are worth 30. To find 1 part you do:
30 ÷ 2 = 15
To find large dressings do:
15 × 3 = 45
To find small dressings do:
15 × 5 = 75
Now you know both large and small totals, you can find the total number of dressings by doing:
45 + 75 = 120 dressings 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.