Final answer:
Sherri has 13 nickels and 3 dimes in her coin purse. This solution was found by setting up a system of equations based on the given relationship between the number of nickels and dimes and their combined value.
Step-by-step explanation:
Sherri is saving nickels and dimes in a coin purse with the total value being $0.95. To find out how many of each coin she has, we create a system of equations based on the information given: The number of nickels (N) is 2 less than 5 times the number of dimes (D). Also, the total value of the coins in the purse is $0.95. Nickels are worth 5 cents and dimes 10 cents.
Let's denote the number of nickels as N and the number of dimes as D. The relationship between the number of nickels and dimes is given as N = 5D - 2. The value equation is 5N + 10D = 95 (since there are 100 pennies in one dollar, and we're working with a value of 95 cents).
Now, we'll substitute the N in the value equation with the expression from the relationship between nickels and dimes. So, 5(5D - 2) + 10D = 95. Simplifying this, we get 25D - 10 + 10D = 95, which simplifies further to 35D - 10 = 95. Solving this equation gives us D = 3. If we have 3 dimes, then the number of nickels is N = 5(3) - 2 = 13.
Thus, Sherri has 13 nickels and 3 dimes in her coin purse.