IGCSE Maths / Ratios and percentages
Ratio word problems revision notes
Edexcel International GCSE Maths (4MA1), chapter 2: Ratios and percentages, specification point 1.7e. Free lesson.
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Ratio word problems are solved by identifying what the given number represents before dividing. It may be one person's share, the difference between two shares, or the whole amount, and each uses a different number of ratio parts.
Find the value of one part from one person's share
The amount you are given is not always the total. If it is one person's share, divide by the number of parts belonging to that person. You can then find other shares and the total. Ann, Bo and Cal share money in the ratio 2 : 3 : 5. Bo's £45 is his 3 parts, not all 10 parts. Check your working by confirming that Bo's share still adds up to £45.
Find one part from the difference between shares
A difference between two shares represents the gap between their ratio parts. Divide the given difference by the difference in the parts, not by the total parts. Sam and Tia share money in the ratio 7 : 4. The difference is 7 − 4 = 3 parts. The £18 difference is 3 parts, so one part is £18 ÷ 3 = £6.
Use the named person's parts in the sports club question
Men, women and children are in the ratio 5 : 4 : 3. The 96 women represent 4 parts, so first find the value of one part. Then use the parts needed for each answer.
Turn a ratio into a fraction of the whole
To find a group's fraction of the whole, put its parts over the total number of parts. You do not need to calculate the actual number in that group. In the club ratio 5 : 4 : 3, men have 5 parts and there are 12 parts altogether. The fraction of the club who are men is 5/12.
Check what the given number counts
Before dividing, decide whether the given number is one person's share, a difference, or the whole amount. Divide by the matching number of ratio parts. One person's share: divide by that person's parts. For example, £45 ÷ 3 = £15. A difference: divide by the difference in parts. For example, £18 ÷ 3 = £6. The whole amount: divide by the total parts. For example, 288 ÷ 12 = 24.