Sally has 21.40 dollars in dimes and quarters for a total of 100 coins. How many of each coin does sally have?

To solve this problem, we can set up a system of equations. Let's represent the number of dimes as "x" and the number of quarters as "y."

From the problem, we know that the total number of coins Sally has is 100, so we have our first equation:

x + y = 100

We also know the total value of Sally's coins is $21.40. The value of one dime is $0.10, and the value of one quarter is $0.25. So, the second equation is:

0.10x + 0.25y = 21.40

To solve this system of equations, we can use substitution or elimination method. Let's solve it using the elimination method:

Multiply the first equation by 0.10 to match the coefficients of x:
0.10(x + y) = 0.10(100)
0.10x + 0.10y = 10

Now, subtract this equation from the second equation:
(0.10x + 0.25y) - (0.10x + 0.10y) = 21.40 - 10
0.15y = 11.40

Divide both sides of the equation by 0.15:
y = 11.40 / 0.15
y = 76

Now, substitute the value of y into the first equation to solve for x:
x + 76 = 100
x = 100 - 76
x = 24

Therefore, Sally has 24 dimes and 76 quarters.

d = 100 - q

25 q + 10 d = 2140

25 q + 1000 -10 q = 2140

15 q = 1140

q = 76
so d = 24