SOLUTION: johnston and betsy have a jar containing 80 coins of which are either quarters or nickels. the total value of the coins is $14.60 how many of each coin do they have? i need the equ

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Question 508033: johnston and betsy have a jar containing 80 coins of which are either quarters or nickels. the total value of the coins is $14.60 how many of each coin do they have? i need the equations please!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels
Let q = number of quarters
given:
(1) +n+%2B+q+=+80+
(2) +5n+%2B+25q+=+1460+ ( in cents )
---------------------
Multiply both sides of (1) by 5
and subtract (1) from (2)
(2) +5n+%2B+25q+=+1460+
(1) +-5n+-+5q+=+-400+
+20q+=+1060+
+q+=+53+
and, since
(1) +n+%2B+q+=+80+
(1) +n+=+80+-+53+
(1) +n+=+27+
They have 27 nickels and 53 quarters
check answer:
(2) +5%2A27+%2B+25%2A53+=+1460+
(2) +135+%2B+1325+=+1460+
(2) +1460+=+1460+
OK