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Home Q & A Board Science-Related Homework Help Mathematics
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nygard93 nygard93
wrote...
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11 years ago
p # of pennies, d dimes, q quarter

p + d +q = 50

p + 10d + 25q = 300

Is there a distinct solution? Or a set of solutions.
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3 Replies
Replies
wrote...
#1
11 years ago
you have 1 degree of freedom, which basically means you can choose a value for one variable and solve the other 2.
if you were to say, graph this as 2 planes, they would intersect at a line, having a set of solutions along that line, but no distinct solutions
Slight Smile
_biology Author
wrote...
#2
11 years ago
You must remember that these are Diophantine equations, i.e. the only acceptable answers are whole numbers because you cannot have a fractional number of coins.

If you subtract the first equation from the second you get 9d + 24q = 250
This has no integer solutions so the original equations have no integer (whole number) solutions.

To put it another way, you cannot have 50 coins which are pennies, dimes and quarters with a total value of $3.
Answer accepted by topic starter
onehowonehow
wrote...
#3
Posts: 9
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11 years ago
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