The Scholarship Fund and the Exchange Rate
A small town scholarship committee has 4 800 € to split among three students. The rules say the amounts must be in the ratio 3 : 4 : 5, and each share must be a whole number of euros. After the split, one member notices that the second student's share, when converted to Hungarian forints at a rate of 1 € = 392 Ft, comes out to a value that is not a multiple of 100 Ft. The committee wants to adjust the ratio slightly to 3 : 4 : 5 but with a small rounding reserve set aside first: they decide to hold back 300 € for bank fees and split the remaining money in the same ratio. A parent asks whether the smallest student's share is still at least 1 200 € after the reserve is removed.
1. Split the full 4 800 € in the ratio 3 : 4 : 5. Are all three shares whole numbers of euros?
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Total parts = 3 + 4 + 5 = 12. One part = 4800 / 12 = 400 €. Shares: 3·400 = 1200 €, 4·400 = 1600 €, 5·400 = 2000 €. Check: 1200 + 1600 + 2000 = 4800 ✓. All three are whole euros, so the original split is valid.
2. After holding back 300 €, split the rest in the ratio 3 : 4 : 5. Does the smallest share stay at or above 1 200 €?
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Remaining money = 4800 − 300 = 4500 €. One part = 4500 / 12 = 375 €. Smallest share = 3·375 = 1125 €. 1125 € is below 1200 €, so the answer is no - the reserve pushes the smallest share under the 1 200 € threshold by 75 €.
3. The second student converts the original 1 600 € share to forints at 392 Ft per euro. Compute the amount in forints and state whether it is a multiple of 100 Ft.
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1600 × 392 = 627 200 Ft. 627 200 ends in 200, so it is a multiple of 100 Ft. The committee member's worry was unfounded: 627200 / 100 = 6272 exactly.