Sierra has a total of 61 dimes and quarters in her piggybank. she has 3 more quarters than dimes. the coins have a total value $10.90. how many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]

Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:

x + y = 61
y = x + 3

Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,
(1/10)x + (1/4)y = 10.90

We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.

x + (x + 3) = 61
Solving for x,
x = 29
y = 29 + 3 = 32

Verifying,
(1/10)(29) + (1/4)(32) = 10.90

Hence, there are 29 dimes and 32 quarters.