Solving a Proportion Application: Currency Exchange from Dollars to Pesos
Apply the proportion-solving strategy to a currency exchange problem.
Problem: Josiah went to Mexico for spring break and changed $325 into Mexican pesos. At that time, the exchange rate was $1 US equal to 12.54 Mexican pesos. How many Mexican pesos did he get for his trip?
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Identify what to find and assign a variable: How many Mexican pesos did Josiah get? Let = the number of Mexican pesos.
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Translate into a proportion, keeping units consistent — dollars over pesos equals dollars over pesos:
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Solve by multiplying both sides by the LCD, 12.54p: Remove common factors on each side. On the left, 12.54 cancels, leaving . On the right, cancels, leaving :
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Check reasonableness: $100 would be 1,254 pesos. Since $325 is a little more than 3 times $100, the answer of 4,075.5 pesos makes sense (roughly , and 4,075.5 is close to that estimate).
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Verify by substituting back into the original proportion: ✓
Answer: Josiah got 4,075.5 Mexican pesos for his spring break trip.
This example demonstrates that proportion problems involving currency exchange follow the same procedure as other proportion applications: align matching units on each side of the proportion (dollars over pesos = dollars over pesos), multiply both sides by the LCD to clear the fractions, and verify the result. The number of pesos is proportional to the number of dollars — when two quantities are related by a proportion, they are said to be proportional.
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