SOLUTION: a coin purse contains 80 cents in nickles and dimes. If there are 12 coins in all,haw many dimes are in the coin purse? i have to use two variables and i am in prealgebra

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Question 453329: a coin purse contains 80 cents in nickles and dimes. If there are 12 coins in all,haw many dimes are in the coin purse?
i have to use two variables and i am in prealgebra
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of nickels
Let b = number of dimes
given:
(1) +a+%2B+b+=+12+
(2) +5a+%2B+10b+=+80+ (in cents)
--------------------
Multiply both sides of (1) by 5
and subtract from (2)
(2) +5a+%2B+10b+=+80+
(1) +-5a+-+5b+=+-60+
+5b+=+20+
+b+=+4+
and, since
(1) +a+%2B+b+=+12+
(1) +a+%2B+4+=+12+
+a+=+8+
There are 4 dimes in the purse
check answer:
(2) +5a+%2B+10b+=+80+
(2) +5%2A8+%2B+10%2A4+=+80+
(2) +40+%2B+40+=+80+
+80+=+80+
OK