#### Answer

We have 22 dimes.
We have 8 nickels.

#### Work Step by Step

Let X represent the number of dimes. Since we have 30 coins, the number of nickels will be 30 - X.
One nickel is worth 5 cents, so we have (30 - X) $\times$ 5 = 150 - 5X cents.
One dime is equal to 10 cents, so we have X $\times$ 10 = 10X cents.
In total, we have 2.60 dollars, which is equal to 260 cents.
We solve the following equation:
150 - 5X + 10X = 260
5X = 110
X = 22
We have 22 dimes.
We have 30 - 22 = 8 nickels.