Trouble with a Linear Diophantine Equation ($4.55 in quarters and dimes)

Steven G

Steven G

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Dec 30, 2014
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Can I get some help on this Linear Diophantine equation, please.
I showed ALL my work but I'm not getting certain answers and I can't figure out why. Please view this video at https://youtu.be/k3e36l4XCPg
 
I haven't read any replies yet. My mistake was not dividing t by gcd(10,25)=5. Now it works fine.
 
BigBeachBanana said:
View attachment 36696

[math]10D + 25Q = 455\\ D=Q\\ 35Q = 455 \implies Q = D = 13[/math]
I don't see how this is a Diophantine problem.
Click to expand...
Yes, and the first thing I did was do it your way. Since this is under the section for Diophantine problem I wanted to use that method because I already new the answer (by using a similar method that you used) and wanted to see if I was using the method correctly. In fact, I learned by knowing the answer before hand that I was making a mistake. Using my method, I only found some of the solutions. Since my method did give me valid solutions I would have thought that I was doing everything correctly except for the fact that I knew that I was supposed to get Q=D =13 and I wasn't.
 
BigBeachBanana said:
View attachment 36696

[math]10D + 25Q = 455\\ D=Q\\ 35Q = 455 \implies Q = D = 13[/math]
I don't see how this is a Diophantine problem.
Click to expand...
The problem does NOT ask about the individual # of quarters & dimes in 4.55, but it asks if it is possible to have EQUAL # of quarters & dimes?

Let us ASSUME that it is possible and let us stack one quarter and one dime. So each stack is valued at 35¢. Can $4.55 be obtained from this stack? We can. We will need 13 stacks ( 455/35 = 13).

This is somewhat "inverse" of reductio ad absurdum!!
 
How do you know the entire problem when the video which states the problem is down? What BBB posted was not the entire problem.
 
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