TGIF. Chris and Terry have been trying to live within their budget but miss going out to dinner on Friday nights. They decide not to spend any nickels or quarters they receive as change for a month and save these in a jar. At the end of the second week they have a total of 165 coins in the jar. The value of the coins totals $23.25. How many nickels are in the jar?
5 n + 25 q = 2325
n + q = 165
To solve this problem, we need to set up a system of equations based on the information given.
Let's assume the number of nickels is represented by 'n' and the number of quarters is represented by 'q'.
Given that the total number of coins in the jar is 165, we can write the equation:
n + q = 165 ---- (Equation 1)
We also know that the total value of the coins is $23.25. Nickels have a value of 5 cents and quarters have a value of 25 cents, so we can write the second equation:
0.05n + 0.25q = 23.25 ---- (Equation 2)
Now, we can solve these equations simultaneously to find the values of 'n' and 'q'.
To eliminate decimals, we can multiply Equation 2 by 100:
5n + 25q = 2325
Now we can use the method of substitution or elimination to solve the system of equations.
Let's solve using elimination:
Multiply Equation 1 by 25 to match the coefficients of 'q':
25(n + q) = 25(165)
25n + 25q = 4125
Now we have the following system of equations:
25n + 25q = 4125 ---- (Equation 3)
5n + 25q = 2325 ---- (Equation 4)
Subtract Equation 4 from Equation 3:
(25n + 25q) - (5n + 25q) = 4125 - 2325
20n = 1800
Divide both sides by 20 to isolate 'n':
n = 1800 / 20
n = 90
Therefore, there are 90 nickels in the jar.