Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many quarters does she have? Write and solve the system of equations.

Sure, let's solve this problem step by step.

First, let's define our variables. Let's say:

D = number of dimes Q = number of quarters

From the problem, we know two things:

1. Sue has 100 coins in total. This can be written as: D + Q = 100
2. The total value of the coins is $21.40. Since dimes are worth$0.10 and quarters are worth $0.25, this can be written as: 0.10D + 0.25Q = 21.40

Now we have a system of two equations, and we can solve it using substitution or elimination. I'll use substitution.

First, let's solve the first equation for D: D = 100 - Q

Now we can substitute (100 - Q) for D in the second equation:

0.10(100 - Q) + 0.25Q = 21.40 10 - 0.10Q + 0.25Q = 21.40 0.15Q = 11.40 Q = 11.40 / 0.15 Q = 76

So, Sue has 76 quarters. To find the number of dimes, we can substitute Q = 76 into the first equation:

D + 76 = 100 D = 100 - 76 D = 24

So, Sue has 24 dimes and 76 quarters.