SOLUTION: Ron has 15 coins with a total value of $1.95. The coins are nickels and quarters. How many of each coin does he have?

Question 1069468: Ron has 15 coins with a total value of $1.95. The coins are nickels and quarters. How many of each coin does he have?

Found 2 solutions by Fombitz, math_helper:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Multiply eq. 1 by 5 and subtract from eq. 2,

Now use either equation to solve for N.

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Since there are two unknown amounts (number of nickels and number of quarters), you should look for two equations.
Let n = number of nickels
and q = number of quarters
"Ron has 15 coins �" and "The coins are nickels and quarters" implies
n + q = 15 (1)
"�total value of $1.95." implies
5n + 25q = 195 (2) (in cents)

There are several approaches to solving these two equations. One is to rearrange (1) and then substitute into (2) to get one equation with one unknown (then later plug back in to get 2nd unknown).
(1) �> q = 15-n (1')
Substitute 15-n for q in (2):
5n + 25(15-n) = 195
5n + 375 - 25n = 195 (distributed the 25)
-20n +375 = 195 (combined like-terms)
-20n = -180 (subtracted 375 from both sides)
n = -180/-20 = 9 (divided both sides by -20)
n=9 �> (from (1')) �> q = 15-9 = 6
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Ans : Ron has 9 nickels and 6 quarters
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Check 9+6 = 15 (ok, good on coin count)
9*5 + 6*25 = 45 + 150 = 195 = $1.95 (ok, good on dollar amount)
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