Question

A vending machine has $13.00 in dimes and quarters. There are 76 coins. How many dimes and how many quarters are in there?

Answer 1

Let +d+ = number of dimes
Let +q+ = number of quarters
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(1) +d+%2B+q+=+76+
(2) +10d+%2B+25q+=+1300+ ( in cents )
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Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10d+%2B+25q+=+1300+
(1) +-10d+-+10q+=+-760+
+15q+=+540+
+q+=+36+
and, since
(1) +d+%2B+q+=+76+
(1) +d+%2B+36+=+76+
(1) +d+=+40+
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There are 40 dimes and 36 quarters
check:
(2) +10%2A40+%2B+25%2A36+=+1300+
(2) +400+%2B+900+=+1300+
(2) +1300+=+1300+