Kevin and Randy Muise have a jar containing
77coins, all of which are either quarters or nickels. The total value of the coins in the jar is $
13.85. How many of each type of coin do they
have?
X Qtrs..
77-x nickels..
25x + 5(77-x) = 1385 cents. X = ?, 77-x = ?.
To solve this problem, we can use a system of equations. Let's represent the number of quarters as "q" and the number of nickels as "n".
1. The total number of coins is 77, so we can set up the equation:
q + n = 77
2. The total value of the coins is $13.85. Since a quarter is worth 25 cents and a nickel is worth 5 cents, we can set up another equation:
0.25q + 0.05n = 13.85
Now, we have a system of equations:
q + n = 77
0.25q + 0.05n = 13.85
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
First, let's multiply both sides of the first equation by -0.05 to make the coefficients of "n" in the two equations cancel each other out:
-0.05q - 0.05n = -3.85
Now, we can add the modified first equation to the second equation:
-0.05q - 0.05n + 0.25q + 0.05n = -3.85 + 13.85
Simplifying the equation, we get:
0.20q = 10
Dividing both sides of the equation by 0.20, we can solve for "q":
q = 50
Now, substitute the value of "q" into the first equation:
50 + n = 77
Solving for "n", we get:
n = 77 - 50
n = 27
Therefore, there are 50 quarters and 27 nickels in the jar.