SOLUTION: A piggy bank has five more dimes than nickels and three less quarters than twice the number of dimes. The total value of the money in the piggy bank is $17.20. Determine how many q

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Question 1033040: A piggy bank has five more dimes than nickels and three less quarters than twice the number of dimes. The total value of the money in the piggy bank is $17.20. Determine how many quarters are in the piggy bank.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +d+=+n+%2B+5+
(2) +q+=+2d+-+3+
(3) +5n+%2B+10d+%2B+25q+=+1720+ ( in cents )
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This si 3 equations and 3 unknowns, so
it's solvable
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(1) +n+=+d+-+5+
Substitute (1) and (2) into (3)
(3) +5%2A%28+d-5+%29+%2B+10d+%2B+25%2A%28+2d-3+%29+=+1720+
(3) +5d+-+25+%2B+10d+%2B+50d+-+75+=+1720+
(3) +65d+=+1820+
(3) +d+=+28+
and
(1) +n+=+d+-+5+
(1) +n+=+28+-+5+
(1) +n+=+23+
and
(2) +q+=+2d+-+3+
(2) +q+=+2%2A28+-+3+
(2) +q+=+56+-+3+
(2) +q+=+53+
there are 53 quarters
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check:
(3) +5n+%2B+10d+%2B+25q+=+1720+
(3) +5%2A23+%2B+10%2A28+%2B+25%2A53+=+1720+
(3) +115+%2B+280+%2B+1325+=+1720+
(3) +1720+=+1720+
OK