Mr. Chang and his wife together had an unpaid balance of $500 on their credit cards for one month. THe bank that issued Mr. Chang's credit card charges an intrest rate of 1.25% a month and his wife's interest is 1.5 per month. If the total interest finance charge was $6.75 how much was each unpaid balance? Write an equaiton for the finance chare and the balance.

If Mr. C owes X, Mrs. C owes 500 - X.

The monthly interest paid is

0.0125X + 0.015*(500 - X) = 6.75

1.25X + 1.5(500 -X) = 675

75 = 0.25 X

Complete the solution for X. Then compute 500 - X

To solve this problem, let's assume that Mr. Chang's credit card balance is represented by 'x' dollars, and his wife's credit card balance is represented by 'y' dollars.

The equation for the finance charge can be derived as follows:

Finance charge for Mr. Chang = Interest rate for Mr. Chang * Mr. Chang's unpaid balance
= 1.25% * x
= (1.25/100) * x
= x/80

Finance charge for Mrs. Chang = Interest rate for Mrs. Chang * Mrs. Chang's unpaid balance
= 1.5% * y
= (1.5/100) * y
= y/66.67

Now, the total finance charge is given as $6.75. So we can set up the equation:

(x/80) + (y/66.67) = 6.75

Now, as mentioned in the problem, the couple had an unpaid balance of $500 for one month. Therefore, the equation for the balances is:

x + y = 500

We have two equations:

(x/80) + (y/66.67) = 6.75
x + y = 500

We can solve this system of equations simultaneously to find the values of x and y.