Question

Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 20 pesos per dollar. While in Mexico, he spends 9000 pesos. When he returns, he exchanges his pesos for dollars (still at 20 pesos per dollar). He gets back 1/10 the amount he started with. Find how many dollars Andre exchanged for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre’s trip using a variable for the number of dollars he exchanged.

Answer 1

Hello!

The answer is:

Andre exchanged 450 dollars for pesos.

Why?

To solve the problem, we need to write two principal equations in order to establish a relation between the number of dollars before and after the trip.

So,

Before the trip, we have:

$Dollars_{beforetrip}*rate=9000pesos\\\\Dollars_{beforetrip}*\frac{20pesos}{1dollar} =9000pesos\\\\Dollars_{beforetrip}=9000pesos\frac{1dollar}{20pesos}=450dollars$

We have that he exchanged 450 dollars for pesos.

Also, we can calculate how many pesos he had before he exchanged it back to dollars, so:

After the trip, we have:

$Pesos{AfterTrip}*rate=\frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}*\frac{1dollar}{20pesos}= \frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}= \frac{1}{10}Dollars_{BeforeTrip}*\frac{20pesos}{1dollar}\\\\Pesos{AfterTrip}= \frac{1}{10}*450dollars*\frac{20pesos}{1dollar}=900pesos$

We have that he had 900 pesos before he exchanged it back to dollars.

Hence, we know that:

Andre exchanged 450 dollars for pesos.

Have a nice day!