SOLUTION: Please help me with this word problem: Johnston and Betsy Warning have a jar containing 80 coins, all of which are either quarters or nickles. The total value of the coins is $14.6

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me with this word problem: Johnston and Betsy Warning have a jar containing 80 coins, all of which are either quarters or nickles. The total value of the coins is $14.6      Log On


   

Question 857922: Please help me with this word problem: Johnston and Betsy Warning have a jar containing 80 coins, all of which are either quarters or nickles. The total value of the coins is $14.60. How many of each type of coin do they have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +q+ = number of quarters
Let +n+ = number of nickels
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(1) +q+%2B+n+=+80+
(2) +25q+%2B+5n+=+1460+ ( in cents )
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Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +25q+%2B+5n+=+1460+
(1) +-5q+-+5n+=+-400+
-----------------------
+20q+=+1060+
+q+=+53+
and, since
(1) +q+%2B+n+=+80+
(1) +n+=+80+-+53+
(1) +n+=+27+
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They have 53 quarters and 27 nickels
check:
(2) +25q+%2B+5n+=+1460+
(2) +25%2A53+%2B+5%2A27+=+1460+
(2) +1325+%2B+135+=+1460+
(2) +1460+=+1460+
OK