SOLUTION: A purse contains $3.75 in 5-cent and 20-cent coins. If there are 33 coins altogether, how many of each type of coin do I have?

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Question 723727: A purse contains $3.75 in 5-cent and 20-cent coins. If there are 33 coins altogether, how many of each type of coin do I have?
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of 5 cent coins
Let +m+ = number of 20 cent coins
--------------
given:
(1) +n+%2B+m+=+33+
(2) +5n+%2B+20m+=+375+ ( in cents )
----------------------
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5n+%2B+20m+=+375+
(1) +-5n+-+5m+=+-165+
+15m+=+210+
+m+=+14+
and, since
(1) +n+%2B+m+=+33+
(1) +n+%2B+14+=+33+
(1) +n+=+19+
19 = number of 5 cent coins
14 = number of 20 cent coins
check answer:
(2) +5n+%2B+20m+=+375+
(2) +5%2A19+%2B+20%2A14+=+375+
(2) +95+%2B+280+=+375+
(2) +375+=+375+
OK

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1 x + 1 y = 33 .............1
Total value
5 x + 20 y = 375 .............2
Eliminate y
multiply (1)by -20
Multiply (2) by 1
-20 x -20 y = -660
5 x + 20 y = 375
Add the two equations
-15 x = -285
/ -15
x = 19
plug value of x in (1)
1 x + 1 y = 33
19 + y = 33
y = 33 -19
y = 14
y = 14
x= 19 number of 5 cent coins
y= 14 number of 20 cent coins