SOLUTION: I have a cup full of change (nickels and quarters). * The value of the coins is $28.95. * There are a total of 187 coins. How many of each coin do I have?

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Question 519277: I have a cup full of change (nickels and quarters).
* The value of the coins is $28.95.
* There are a total of 187 coins.
How many of each coin do I have?
Found 2 solutions by mananth, oberobic:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
nickels x coins
quarters y coins

1 x + 1 y = 187 .............1
5 x + 25 y = 2895 .............2
Eliminate y
multiply (1)by -25
Multiply (2) by 1
-25 x -25 y = -4675
5 x 25 y = 2895
Add the two equations
-20 x = -1780
/ -20
x = 89
plug value of x in (1)
1 x + 1 y = 187
89 + 1 y = 187
1 y = 187 -89
1 y = 98
y = 98

m.ananth@hotmail.ca

Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
With coin problems you have to keep track of the number of coins and their value.
n = number of nickels
5n = value of the nickels in cents
q = number of quarters
25q = value of the quarters in cents
.
n + q = 187 coins
so
n = 187-q
.
5n + 25q = 2895 cents
.
substitute
.
5(187-q) + 25q = 2895
935 -5q +25q = 2895
20q = 1960
q = 98
.
n = 187-q
n = 89
.
Check their values
5(89) = 445 cents
25(98) = 2450 cents
445+2450 = 2895 cents
Correct.
.
Answer: You have 98 quarters and 89 nickels.
.
Done.