A woman has $1.70 in dimes and nickels. She has 5 more dimes than nickels. How many nickels

does she have?

let .05x = number of nickels and .10x = number of dimes

5(.10x) + .05x = 1.70

multiply both sides by 100

50x + 5x = 170

55x = 170

To solve this problem, we will create a system of equations based on the given information. Let's assume that the woman has x nickels and x+5 dimes.

Since the value of a nickel is $0.05, the total value of nickels in cents can be calculated as 5x.

Similarly, the value of a dime is $0.10, so the total value of dimes in cents can be calculated as 10(x+5).

Adding the values of nickels and dimes, we can write the equation:

5x + 10(x+5) = 170

To solve this equation, we will simplify and solve for x.

5x + 10x + 50 = 170
15x + 50 = 170
15x = 120
x = 8

Therefore, the woman has 8 nickels.

13 dimes 8 nickels