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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