A hard question on sum and multiple for P5, with a step-by-step solution, diagrams and the answer. Sum-and-multiple and difference-and-multiple questions appear in the Hua Xia Cup's P3 to P5 first rounds, qualifying rounds and finals.
The question
A brother, a sister and their little brother have $176 of pocket money in all.
The big brother has $2 more than twice the little brother's money.
The sister has $5 less than twice the big brother's.
How much does the sister have?
Show the hints (3)
💡Hint 1: Who has the least? Try writing the others' money in terms of his.
💡Hint 2: Big brother = 2 × little brother + $2; sister = 2 × big brother − $5 = 4 × little brother + $4 − $5.
💡Hint 3: The little brother has $25 and the big brother $52.
Worked solution
Have a go first, then read the solution step by step.
1.Little brother = 1 part: big brother = 2 parts + $2. The sister is two big brothers less $5: 4 parts + $2 + $2 − $5.
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