You have 50 coins, all quarter's and dimes. How would you know how many of each coin and come up with a total of 11.15$-?

so, why do you say "quarter's" and not "dime's"?

Rule of thumb: MOST plurals do not include an apostrophe!

I would know how many of each by solving:

q+d = 50 and
25q + 10d = 1115

go for it

And why are you placing the dollar sign after the number? It should read ~~> $11.15 (or whatever the correct answer is).

To determine the number of quarters and dimes you have, as well as the total value, you can use a system of equations.

Let's suppose the number of quarters is represented by "q" and the number of dimes by "d". The total value in dollars can be represented as "t=11.15".

We know that the value of a quarter is $0.25 and the value of a dime is $0.10. From this, we can create two equations:

1) The total number of coins equation: q + d = 50
2) The total value equation: 0.25q + 0.10d = 11.15

Now, we can solve these equations simultaneously to find the values of q and d. There are several methods you can use to solve this system of equations, such as substitution or elimination. I will use substitution in this explanation:

First, isolate one variable in the first equation. Let's solve for q:
q = 50 - d

Next, substitute this expression for q in the second equation:
0.25(50 - d) + 0.10d = 11.15

Simplify and solve for d:
12.5 - 0.25d + 0.10d = 11.15
12.5 - 0.15d = 11.15
-0.15d = 11.15 - 12.5
-0.15d = -1.35
d = -1.35 / -0.15
d = 9

Now that we have the value of d, we can substitute it back into the first equation to find q:
q + 9 = 50
q = 50 - 9
q = 41

Therefore, you have 41 quarters and 9 dimes.

To verify the total value, substitute these values into the total value equation:
0.25(41) + 0.10(9) = 11.15
10.25 + 0.90 = 11.15 (which is approximately equal to 11.15)

Hence, you have 41 quarters, 9 dimes, and the total value is $11.15.