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.