Chain-link conversion for money

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The discussion revolves around a currency conversion problem involving U.S. dollars, European euros, and Japanese yen. The initial attempt at a chain-link conversion incorrectly used the relationship between yen and euros, leading to an erroneous conclusion that one U.S. dollar equals 0.00556 yen. The correct understanding is that one yen equals 0.00776 euros, not the other way around. This misunderstanding was clarified by a participant, leading to the realization of the mistake. Accurate currency conversion is crucial for correct financial calculations.
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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!
 
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