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?
You need two equations to substitute into each other. You need one for the total number of coins, and one for the amount.
d=# of dimes
q=# of quarters
d+q=100
.10d+.25q=14.05
Get how I got those equations? See if you can solve the rest. If you can't, post again, and I'll see if I can help you.
need help
56
To solve the system of equations, you can use the method of substitution or elimination.
Let's start by solving the first equation, d + q = 100, for d in terms of q:
d = 100 - q
Now substitute this expression for d into the second equation:
0.10d + 0.25q = 14.05
0.10(100 - q) + 0.25q = 14.05
10 - 0.10q + 0.25q = 14.05
Combine like terms:
0.15q = 4.05
Divide both sides by 0.15 to solve for q:
q = 4.05 / 0.15 = 27
Marcy has 27 quarters.