Question

7TH GRADE MATH

a parking meter contains 6.25 in dimes and quarters. if the number of dimes is 2 more than 3 times the number of quarters, how many of each coin are in the parking meter?

Answer 1

11 quarters and 35 dimes

Explanation:

We can create a system of equations to find the number of both dimes and quarters that are in the parking meter.

1st equation: We know that the value of a dime ($0.10) * the number of dimes (D) + the value of a quarter ($0.25) * the number of quarters (Q) = $6.25

2nd equation: If we allow D to represent dimes and Q to represent quarters, the number of dimes = 3 times the number of quarters is 3Q and 2 more than this is 3Q + 2

Thus, our two equations are:

0.10D + 0.25Q = 6.25

D = 3Q + 2

The equations are already set up in a way where we can use substitution to solve and substitute the formula for D in the second equation for D in the first equation:

`0.10(3Q+2)+0.25Q=6.25\\0.30Q+0.20+0.25Q=6.25\\0.20+0.55Q=6.25\\0.55Q=6.05\\Q=11`

Now that we've found the number of quarters, we can use either equation to find the number of dimes:

`D=3(11)+2\\D=33+2\\D=35`

It's always helpful to check the solutions (time-permitting) in both equations to make sure our math was accurate

1st equation:

0.10(35)+0.25(11)=6.25

3.50 + 2.75 = 6.25

6.25 = 6.25

2nd equation:

35 = 3(11) + 2

35 = 33 + 2

35 = 35