Sierra has a total of 61 dimes and quarters. she has 3 more quarters than dimes. the coins have a value of $10.90. how many quarters and dimes does she have? [hint: use the decimal values of the c coins to write an equation.] (the instructions say "write an equation and use the equation to solve the problem.")

Let the number of dimes be x and the number of quarters be y, then
x + y = 61 . . . . . . . . . . . .(1)
0.1x + 0.25y = 10.90 . . . (2)

From (1): x = 61 - y . . . . .(3)

Putting (3) into (2) gives: 0.1(61 - y) + 0.25y = 10.90
6.1 - 0.1y + 0.25y = 10.90
6.1 + 0.15y = 10.90
0.15y = 10.90 - 6.1 = 4.80
y = 4.80/0.15 = 32
x = 61 - 32 = 29

Therefore, there are 29 dimes and 32 quarters