marcy has a total of 100 dimes and quarters. if the total value of the coins is $14.05, how many quarters does she have?
let d = the number of dimes, and q = the number of quarters.
d + q = 100
0.10d + 0.25q = 14.05
27
To determine the number of quarters Marcy has, we need to set up an equation. Let's represent the number of quarters as "q" and the number of dimes as "d".
We are given two pieces of information:
1. The total number of dimes and quarters is 100: q + d = 100
2. The total value of the coins is $14.05: 0.25q + 0.10d = 14.05
Now we can solve this system of equations to find the value of "q", representing the number of quarters.
First, let's solve the first equation for "d":
q + d = 100
d = 100 - q
Now substitute this value of "d" into the second equation:
0.25q + 0.10(100 - q) = 14.05
Simplify the equation:
0.25q + 10 - 0.10q = 14.05
0.15q = 14.05 - 10
0.15q = 4.05
Divide both sides by 0.15 to isolate "q":
q = 4.05 / 0.15
q ≈ 27
Therefore, Marcy has approximately 27 quarters.