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Math problem about sharing sweets in ratios.

$Alice and Olivia share sweets in the ratio 7:3, after Alice gives 3 sweets to Olivia, the ratio becomes 5:3; find initial amounts.$

Alice and Olivia share sweets in the ratio 7:3, after Alice gives 3 sweets to Olivia, the ratio becomes 5:3; find initial amounts.

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Show Answer Key & Explanations Step-by-step solution for: Resourceaholic: New GCSE: Ratio

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- Let the initial number of sweets Alice has be 7x and Olivia has be 3x.
- After Alice gives 3 sweets to Olivia, Alice has 7x - 3 and Olivia has 3x + 3.
- The new ratio is (7x - 3) : (3x + 3) = 5 : 3.
- Set up the equation: (7x - 3)/(3x + 3) = 5/3.
- Cross-multiply: 3(7x - 3) = 5(3x + 3).
- Simplify: 21x - 9 = 15x + 15.
- Subtract 15x from both sides: 6x - 9 = 15.
- Add 9 to both sides: 6x = 24.
- Divide by 6: x = 4.
- Alice initially had 7x = 7 * 4 = 28 sweets.
- Olivia initially had 3x = 3 * 4 = 12 sweets.

Parent Tip: Review the logic above to help your child master the concept of math ratio problems.

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