Chain-link conversion for money

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SUMMARY

The discussion centers on a chain-link conversion problem involving currency exchange rates. The user incorrectly calculated the conversion from U.S. dollars to Japanese yen by misinterpreting the relationship between euros and yen. The correct conversion should use the fact that 1 yen equals 0.00776 euros, not the other way around. Consequently, the accurate conversion shows that one U.S. dollar is equivalent to 90.9 yen.

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Mr Davis 97
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Homework Statement


I have the following question to answer: "A U.S. dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How much Japanese yen equals a U.S. dollar?"

Homework Equations

The Attempt at a Solution


To solve the problem, I tried chain-link conversion (as would be done with physics quantities):

##
\displaystyle1US ~ \cdot ~ \frac{0.716euro}{1US} ~ \cdot ~ \frac{0.00776yen}{1euro}
##

Multiplying this out, I get 0.00556. Which should mean that 1 dollar is equivalent to 0.00556 yen. However, the answer is that one U.S. dollar is equivalent to 90.9 yen. What am I doing wrong?
 
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Mr Davis 97 said:

Homework Statement


I have the following question to answer: "A U.S. dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How much Japanese yen equals a U.S. dollar?"

Homework Equations

The Attempt at a Solution


To solve the problem, I tried chain-link conversion (as would be done with physics quantities):

##
\displaystyle1US ~ \cdot ~ \frac{0.716euro}{1US} ~ \cdot ~ \frac{0.00776yen}{1euro}
##

Multiplying this out, I get 0.00556. Which should mean that 1 dollar is equivalent to 0.00556 yen. However, the answer is that one U.S. dollar is equivalent to 90.9 yen. What am I doing wrong?
Your conversion has 0.00776 yen = 1 euro, which is bass ackwards from the problem statement that 1 yen = 0.00776 euro.
 
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SteamKing said:
Your conversion has 0.00776 yen = 1 euro, which is bass ackwards from the problem statement that 1 yen = 0.00776 euro.
Oh, wow. I feel stupid. Thanks!