There are 9 more quarter then dimes.if the total value of the coins is 6.8, how ,any quarters are there?

Is the total value $6.80?

If so, then let Q be the number of quarters and D be the number of dimes.

You know that
Q -D = 9, and
0.25Q + 0.1D = 6.80
Solving bu substitution,
0.25Q + 0.1(Q-9) = 6.80
0.35Q = 7.70
Q = 22
Now solve for D

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To determine the number of quarters, we need to set up a system of equations based on the information given.

Let's represent the number of dimes as "d" and the number of quarters as "q."

From the first statement, we know that there are 9 more quarters than dimes, so we can write the equation: q = d + 9.

The value of each dime is $0.10, and the value of each quarter is $0.25. The total value of the coins is $6.80. So, we can write another equation based on the total value: 0.10d + 0.25q = 6.80.

Now, we have a system of two equations:
q = d + 9
0.10d + 0.25q = 6.80

To solve this system, we can substitute the value of q from the first equation into the second equation:

0.10d + 0.25(d + 9) = 6.80

Next, we can distribute 0.25 into the expression (d + 9):

0.10d + 0.25d + 2.25 = 6.80

Combine like terms:

0.35d + 2.25 = 6.80

Subtract 2.25 from both sides:

0.35d = 4.55

Divide both sides by 0.35:

d = 4.55 / 0.35 = 13

Therefore, there are 13 dimes.

Using the first equation, we can find the number of quarters:

q = d + 9 = 13 + 9 = 22

So, there are 22 quarters.