SOLUTION: your uncle juan has a piggy bank which has 110 coins in quarters and dimes only.he wants to give you all the money if you can tell him the exact number of quarters and the exact nu

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Question 720739: your uncle juan has a piggy bank which has 110 coins in quarters and dimes only.he wants to give you all the money if you can tell him the exact number of quarters and the exact number of dimes given that there is $21.65 in the piggy bank.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = number of dimes
Let +q+ = number of quarters
given:
(1) +d+%2B+q+=+110+
(2) +10d+%2B+25q+=+2165+
------------------------
Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10d+%2B+25q+=+2165+
(1) +-10d+-+10q+=+-1100+
+15q+=+1065+
+q+=+71+
and, since
(1) +d+%2B+q+=+110+
(1) +d+%2B+71+=+110+
(1) +d+=+39+
The number of dimes is 39
The number of quarters is 71
check:
(2) +10%2A39+%2B+25%2A71+=+2165+
(2) +390+%2B+1775+=+2165+
(2) +2165+=+2165+
OK