a purse contain $6.00 in quarters and dimes. there are 17 more quarters than dimes. find the number of quarters and dimes

number of dimes --- x

number of quarters --- x+17

value of money:
10x + 25(x+17) = 600 , all in cents
10x + 25x + 425 = 600
35x = 175
x = 5

so 5 dimes and 22 quarters.

check by finding the value of 5 dimes and 22 quarters.

To find the number of quarters and dimes, we can set up a system of equations.

Let's assume the number of dimes is "x". Since the number of quarters is 17 more than the number of dimes, we can represent the number of quarters as "x + 17".

Now, let's convert the value of quarters and dimes into cents, as it will be easier to compute. One quarter is equal to 25 cents, and one dime is equal to 10 cents. So, the value of the quarters in cents is 25(x + 17), and the value of the dimes in cents is 10x.

According to the problem, the sum of the values of quarters and dimes is $6.00, which is equal to 600 cents. Therefore, we can write the equation:

25(x + 17) + 10x = 600

Now, let's solve the equation for x to find the number of dimes:

25x + 425 + 10x = 600
35x + 425 = 600
35x = 600 - 425
35x = 175
x = 175/35
x = 5

So, the number of dimes is 5.

Since the number of quarters is 17 more than the number of dimes, the number of quarters is x + 17, which is 5 + 17 = 22.

Therefore, there are 22 quarters and 5 dimes in the purse.