Problem 8 · 1995 AJHSME
Medium
Ratios, Rates & Proportions
proportion
An American traveling in Italy wishes to exchange American dollars for Italian lire. If 3000 lire = $1.60, how much lire will the traveler receive for $1.00?
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Answer: D — 1875 lire.
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Hint 1 of 2
You're given lire for $1.60 but asked for lire per $1.00. Find the 'per one dollar' rate — that's the unit rate, and a unit rate makes every later question easy.
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Hint 2 of 2
To get the rate for exactly $1, divide the lire by the number of dollars: 3000 ÷ 1.60.
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Approach: find the unit rate (lire per single dollar)
- The whole game is to find how many lire one dollar buys — the unit rate. Once you have 'per $1,' any dollar amount is just a multiply.
- $1.60 → 3000 lire, so $1.00 → 3000 ÷ 1.60 = 1875 lire.
- Sanity check: $1 is less than $1.60, so you should get fewer than 3000 lire — and 1875 < 3000. Good. (Choice 4875 is the trap of multiplying instead of dividing.)
- Why this transfers: exchange rates, unit prices, and speeds all become trivial once you reduce them to 'per one' first.
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