Answer:
Gina has 47 nickels
Explanation:
Let's call the number of nickels that Gina has "n" and the number of dimes she has "d". We know that she has a total of 70 nickels and dimes, so:
n + d = 70 (equation 1)
We also know that the value of her nickels and dimes is $4.65, which is equal to 465 cents. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value of n nickels is 5n cents and the value of d dimes is 10d cents. Therefore, we can write another equation based on the value of the coins:
5n + 10d = 465 (equation 2)
We can simplify equation 2 by dividing both sides by 5:
n + 2d = 93 (equation 3)
Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable. For example, we can solve equation 1 for d:
d = 70 - n
Substituting this expression for d into equation 3, we get:
n + 2(70 - n) = 93
Simplifying this equation, we get:
n + 140 - 2n = 93
-n + 140 = 93
-n = -47
n = 47
Therefore, Gina has 47 nickels and 23 dimes (since n + d = 70), and the total value of her coins is $4.65.