SOLUTION: johnston and betsy waring have a jar containing 80 coins all of which are either quarters or nickels.The total value of the coins is $14.60. How many of each type of coin do they h

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: johnston and betsy waring have a jar containing 80 coins all of which are either quarters or nickels.The total value of the coins is $14.60. How many of each type of coin do they h      Log On


   

Question 621577: johnston and betsy waring have a jar containing 80 coins all of which are either quarters or nickels.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 +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+%2B+53++=+80+
(1) +n+=+27+
They have 27 nickels and 53 quarters
check:
(2) +5%2A27+%2B+25%2A53+=+1460+
(2) +135+%2B+1325+=+1460+
(2) +1460+=+1460+
OK