John is planning to tour Europe after college. He wants to know if he has enough money. He found out that he can exchange 15 dollars for 12 euros. At this exchange rate, approximately how many euros should he get in exchange for 100 dollars?
Our exchange rate is a ratio of dollars to euros, 15 dollars to 12 euros. We can use this information to find out how many euros one dollar is. If 15 dollars is 12 euros, we divide 15 by 15 to get one. And we divide 12 by 15 to get the number of euros one dollar would buy.
For our next step, we can simplify the fraction twelve fifteenths. Both the numerator and the denominator are divisible by three. Twelve fifteenths simplifies to four-fifths. One dollar equals four-fifths of a euro. And we want to know about 100 dollars. We take one and multiply it by 100. And we’ll get 100 dollars. But to keep our ratio equal, we’ll have to do the same thing on the right-hand side. We’ll need to multiply four-fifths by 100. That means we multiply the numerator four times 100. And the denominator stays the same. It is 400 over five euros, 100 dollars to 400 over five euros. If we divide 40 by five, we get eight. And that means 400 divided by five is 80. And so we can say that 100 dollars is 80 euros.
We set this ratio up and solved. However, we could also set this up with fractions. The fraction would look like this. 15 dollars over 12 euros equals 100 dollars over 𝑥. The first thing we do is simplify our fraction 15 over 12. If we divide 15 by three, we get five. And 12 by three, we get four. Five over four equals 100 over 𝑥. And we know that you multiply 20 by five to get 100. And that means we would need to multiply four by 20 to find out how many euros that would be equal to. 𝑥 equals four times 20. 𝑥 equals 80.
Both methods show that John would get 80 euros in exchange for 100 dollars.