SOLUTION: how to solve this problem: A class contributed $19.00 in quarters and dimes to the Red Cross. In all their 100 coins. How many were there of each card?

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Question 1078087: how to solve this problem:
A class contributed $19.00 in quarters and dimes to the Red Cross. In all their 100 coins. How many were there of each card?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = number of dimes
Let +q+ = number of quarters
---------------------------------
(1) +d+%2B+q+=+100+
(2) +10d+%2B+25q+=+1900+ ( in cents )
-----------------------------------
(2) +2d+%2B+5q+=+380+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2d+%2B+5q+=+380+
(1) +-2d+-+2q+=+-200+
-------------------------
+3q+=+180+
+q+=+60+
and
(1) +d+%2B+q+=+100+
(1) +d+%2B+60+=+100+
(1) +d+=+40+
-----------------------
There are 40 dimes and 60 quarters
-----------------------------------
check:
(2) +10d+%2B+25q+=+1900+
(2) +10%2A40+%2B+25%2A60+=+1900+
(2) +400+%2B+1500+=+1900+
(2) +1900+=+1900+
OK