SOLUTION: A parking meter contains quarters and nickels worth ​$13.45. There are 89 coins in all. Find how many of each there are.

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Question 1162718: A parking meter contains quarters and nickels worth ​$13.45. There are 89 coins in all. Find how many of each there are.

Found 3 solutions by Boreal, VFBundy, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x quarters
89-x nickels
.25x+.05(89-x)=13.45
.25x+4.45-0.05x=13.45
0.20x=9.00
x=45 quarters ($11.25)
89-x=44 nickels ($2.20)
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
Number of quarters = q
Number of nickels = n

q + n = 89
0.25q + 0.05n = 13.45

Multiply first equation by -0.05:

-0.05q - 0.05n = -4.45
0.25q + 0.05n = 13.45

Add both equations together and solve for q:

0.20q = 9

q = 45

Since q = 45...and q + n = 89...that means n = 44.

Number of quarters = q = 45
Number of nickels = n = 44
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let's use cents instead of dollars so we don't have to write all those decimals. The total value of the coins is 1345 cents.

If a formal algebraic solution is not required, and if you are good with mental math, then this problem can be solved quickly and easily using logical reasoning.

If the 89 coins were all nickels, the value would be $4.45, or 445 cents.
The actual value, 1345 cents, is 900 cents more than that.
Trading a nickel for a quarter keeps the number of coins at 89 but increases the total value by 25-5 = 20 cents.
To make up the addition 900 cents, the number of quarters you need is 900/20 = 45.

ANSWER: 45 quarters, and 89-45 = 44 nickels.

CHECK: 45(25)+44(5) = 1125+220 = 1345
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