SOLUTION: The total value of the quarters and dimes in a coin bank is $8.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $8.60. Find the n

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Question 720582: The total value of the quarters and dimes in a coin bank is $8.90. If the quarters were dimes and the
dimes were quarters, the total value of the coins would be $8.60. Find the number of quarters in the
bank.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the number of dimes
Let +q+ = the number of quarters
given:
(1) +10d+%2B+25q+=+890+ ( in cents )
(2) +10q+%2B+25d+=++860+
-----------------------
Rewrite the equations
(1) +2d+%2B+5q+=+178+
(2) +5d+%2B+2q+=+172+
---------------------
Multiply both sides of (1) by
+5+ and both sides of (2)
by +2+ then subtract (2) from (1)
------------------------------
(1) +10d+%2B+25q+=+890+
(2) +-10d+-4q+=+-344+
+21q+=+546+
+q+=+26+
and
(1) +2d+%2B+5q+=+178+
(1) +2d+%2B+5%2A26+=+178+
(1) +2d+=+178+-+130+
(1) +2d+=+48+
(1) +d+=+24+
The number of dimes in the bank is 24
The number of quarters in the bank is 26
check:
(2) +10q+%2B+25d+=++860+
(2) +10%2A26+%2B+25%2A24+=+860+
(2) +260+%2B+600+=+860+
(2) +860+=+860+
OK