Problem 27 · 2019 Math Kangaroo
Stretch
Ratios, Rates & Proportions
ratio
Ria and Flora compare their savings and find that they are in the ratio 5 : 3. Then Ria buys a tablet for 160 €. The ratio of their savings now changes to 3 : 5. How much money did Ria have before she bought the tablet?
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Answer: C — 250 €
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Hint 1 of 2
Write both savings using the 5 : 3 ratio with one unknown.
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Hint 2 of 2
Subtract 160 from Ria's and set the new ratio to 3 : 5.
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Approach: set the changed ratio equal to 3 : 5
- Let savings be 5x (Ria) and 3x (Flora).
- After Ria spends 160: (5x − 160) : 3x = 3 : 5, so 5(5x − 160) = 9x.
- That gives 25x − 800 = 9x, 16x = 800, x = 50, so Ria had 5x = 250 Euros.
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