The ratio of dimes to nickels in jan's change box is 2/3. jan has 75 cents in nickles. how many nickes does jan have? 15? would that be correct?

and would she have 10 dimes?

Yes to both answers.

To find the number of dimes and nickels Jan has, we can set up a ratio with the given information.

Given:
Ratio of dimes to nickels = 2/3
Value of nickels = 75 cents

Step 1: Determine the value of one nickel
Since Jan has 75 cents in nickels and the value of one nickel is 5 cents, we divide the total value by the value of one nickel:
75 cents / 5 cents = 15

Jan has 15 nickels.

Step 2: Determine the number of dimes
Using the ratio, we can compare the number of dimes to nickels. The ratio of dimes to nickels is given as 2/3.

Let's assume the number of dimes is x.
So, the ratio becomes:
x / 15 = 2 / 3

Now we can solve for x by cross-multiplying:
3x = 2 * 15
3x = 30

Divide both sides of the equation by 3:
x = 30 / 3
x = 10

Jan has 10 dimes, not 15.

To find the number of nickels Jan has, you should first determine the value of one nickel. Since it is given that Jan has 75 cents in nickels, the value of one nickel would be 75 cents divided by the number of nickels.

Let's assume the number of nickels is "n". So, the equation would be:
Value of one nickel = 75 cents / n

Since the ratio of dimes to nickels is 2/3, you can express the number of dimes in terms of the number of nickels. The equation would be:
Number of dimes = (2/3) * n

Now, to confirm if Jan has 15 nickels, we can substitute n = 15 into the equations.

Value of one nickel = 75 cents / 15 = 5 cents
Number of dimes = (2/3) * 15 = 10 dimes

Therefore, your calculations are correct. Jan has 15 nickels and 10 dimes.