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