SOLUTION: I have a jar containing 89 coins. All of the coins are nickels and quarters. The total value of the coins in the jar is $13.05. How many quarters, and how many nickels do I have?

Question 980097: I have a jar containing 89 coins. All of the coins are nickels and quarters. The total value of the coins in the jar is $13.05. How many quarters, and how many nickels do I have?
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
In order to solve this word problem, we need to set up a system of linear equations.

We know that a nickel is worth .05 cents and a quarter is worth .25 cents. We also know that the total value of the coins is $13.05, so, our first equation will be:

.05n + .25q = 13.05 (n stands for nickels and q stands for quarters)

We know that there are a total of 89 coins. So, our second equation will be:

n + q = 89

Now we have our system of linear equations:

.05n + .25q = 13.05
n + q = 89

To make this easier to solve, let's multiply our first equation by 100, which will eliminate all the decimals. We will then have

5n + 25q = 1305
n + q = 89

Now, we need to eliminate one of our variables. Since 5 is easier to work with than 25, let's multiply our second equation by -5 and then add both equations together:

5n + 25q = 1305
-5n -5q = -445

5n - 5n + 25q - 5q = 1305 - 445 -----> 20q = 860

Now, divide both sides by 20 and we will have our number of quarters:

q = 860/20 -----> q = 43

Therefore, we have 43 quarters.

To find out how many nickels we have, replace the q in our original second equation with 43 and solve:

n + 43 = 89 -----> n = 89 - 43 -----> n = 46

Therefore, we have 46 nickels.

We can verify that our answer is correct by replacing in our first original equation the n and q with 46 and 43, respectively:

.05(46) + .25(43) = 13.05 -----> 2.30 + 10.75 = 13.05 -----> 13.05 = 13.05

Since 13.05 is equal to 13.05, our answer is correct.

Answer: 46 nickels and 43 quarters

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