SOLUTION: Julie has $3.10 in change in her pocket. If she has only 50 cents and 20 cents pieces and the total number of coins are 11, how many coins of each type does she have?

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Question 1140432: Julie has $3.10 in change in her pocket. If she has only 50 cents and 20 cents pieces and the total number of coins are 11, how many coins of each type does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 20 cent coins
Let +b+ = number of 50 cent coins
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(1) +a+%2B+b+=+11+
(2) +20a+%2B+50b+=+310+ ( in cents )
--------------------------------------------
(2) +2a+%2B+5b+=+31+
Multiply both sides of (2) by +2+
and subtract (1) from (2)
(2) +2a+%2B+5b+=+31+
(1) +-2a+-+2b+=+-22+
---------------------------
+3b+=+9+
+b+=+3+
and
(1) +a+%2B+3+=+11+
(1) +a+=+8+
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She has 8 of the 20 cent coins and
3 of the 50 cent coins
check:
(2) +2%2A8+%2B+5%2A3+=+31+
(2) +16+%2B+15+=+31+
(2) +31+=+31+
OK