Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin doe

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have?

Set up two equations where d is the number of dimes and q is the number of quarters:
(1) d + q = 10
(2) 0.1d + 0.25q = 1.45

Rearrange (1) into (3) to solve for d
(3) d = 10 - q

Now plug (3) into (2)
0.1(10 - q) + 0.25q = 1.45

Multiply through:
1 - 0.1q + 0.25q = 1.45

Combine q terms
0.15q + 1 = 1.45

Subtract 1 from each side
0.15q = 0.45

Divide each side by 0.15
q = 3

Plug our q = 3 value into (3)
d = 10 - 3
d = 7