(adsbygoogle = window.adsbygoogle || []).push({}); 1. A Japanese businessman returning from a trip in North America exchanges his US and Canadian dollars for yen. If he receives 15286 yen, and received 122 yen for each US and 112 yen foer eac Canadian dollar, how many of each type of currency did he exchange?

2. I know in solving this type of equations you find the gcd, I did that but I did not get the exact answer as the book did

3. Let x = #of yens for each US and y = # of ens for each Canadian

122 x + 112 y = 15286

the gcd(122,112) = 2 which divides 15286

by using the Euclidean Algorithm I found x to be -11 and y = 12

so I have 122(-11) 7643 + 112(12) 7643 = (2) 7643

122(-84073) + 112(91716) = 15286, along with other solutions x = -84073 + 112t and y = 91716 - 122t, which I think does not apply here...

the book's answer is 39 US and 94 Cand or 95 US and 33 Cand.

From this it seems as if they just used the Euclidean Algorithm without incorporating the gcd...

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# Homework Help: Linear Diophantine Equations

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