tom has 17 coins in his pocket worth $1.30. If he has only dimes and nickles, how many coins of each does he have?

number of dimes ---> x

number of nickels ---> 17-x)

solve for x .....

10x + 5(17-x) = 130

8 nickels 9 dimes

To find out how many coins of each type Tom has, we can set up a system of equations based on the given information.

Let's assume Tom has x number of nickels and y number of dimes.

Since Tom has 17 coins in total, we can write the equation:
x + y = 17 --(Equation 1)

We also know that the value of the coins is $1.30. The value of a nickel is $0.05, and the value of a dime is $0.10. So, we can write the second equation as:
0.05x + 0.10y = 1.30 --(Equation 2)

To solve these equations, we can use the substitution method or the elimination method. In this case, let's solve it using the elimination method:

First, let's multiply Equation 1 by 0.05 to eliminate the variable x:
0.05(x + y) = 0.05(17)
0.05x + 0.05y = 0.85 --(Equation 3)

Next, let's subtract Equation 3 from Equation 2 to eliminate the x variable:
0.05x + 0.10y - (0.05x + 0.05y) = 1.30 - 0.85
0.05y = 0.45

To isolate y, we divide both sides of the equation by 0.05:
0.05y / 0.05 = 0.45 / 0.05
y = 9

Now that we have the value of y, let's substitute it back into Equation 1 to find x:
x + 9 = 17
x = 17 - 9
x = 8

Therefore, Tom has 8 nickels and 9 dimes.