A medium question on ratios for P5–P6, with a step-by-step solution, diagrams and the answer. Ratio questions appear in the Hua Xia Cup's P4 to P6 first rounds, qualifying rounds and finals, such as linked ratios and ratios that change.
The question
Classes A, B and C took part in a flag day to raise money.
The amounts raised by class A and class B are in the ratio 5 :
4, and the amounts raised by class B and class C are in the ratio 5 :
3.
The three classes raised $5700 in all.
How much did class A raise?
Show the hints (2)
💡Hint 1: Class B appears in both ratios. How many parts is it in each? Are those parts the same size?
💡Hint 2: Make class B the same number of parts in both (a common multiple of 4 and 5), then write class A : class B : class C.
Worked solution
Have a go first, then read the solution step by step.
1.Class B is 4 parts in the first ratio and 5 parts in the second. It is the same amount cut into different numbers of parts, so the parts differ in size and can't simply be joined.
2.Cut class B again into 20 parts, the lowest common multiple of 4 and 5: Class A : class B = 5 : 4 = 25 : 20; class B : class C = 5 : 3 = 20 : 12. Now every part is the same size.
3.So class A : class B : class C = 25 : 20 : 12: 25 + 20 + 12 = 57 parts in all.
4.57 parts are 5700, so 1 part = 5700 ÷ 57 = 100.
5.Class A raised 25 × 100 = $2500.
⚠️Common mistake: writing class A : class B : class C = 5 : 4 : 3. Class B is 4 parts in one ratio and 5 in the other, so they can't simply be joined.
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