SOLUTION: Moya has a total of $3.10 in her pocket in only 10 and 20 cent coins. If she has 19 coins altogether, how many of each coin does she have? Please show working.

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Question 889855: Moya has a total of $3.10 in her pocket in only 10 and 20 cent coins. If she has 19 coins altogether, how many of each coin does she have?
Please show working.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 10 cent coins she has
Let +b+ = number of 20 cent coins she has
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(1) +10a+%2B+20b+=+310+
(2) +a+%2B+b+=+19+
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Multiply both sides of (2) by +10+
and subtract (2) from (1)
(1) +10a+%2B+20b+=+310+
(2) +-10a+-+10b+=+-190+
+10b+=+120+
+b+=+12+
and, since
(2) +a+%2B+12+=+19+
(2) +a+=+7+
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She has 7 of the 10 cent coins
She has 12 of the 20 cent coins