If the total finance charge for both Greg and his wife was $9.00, how much was each unpaid balance?

Question

This is from Chapter 5, Exercise 5-3, #15 of Fundamentals of Technical Mathematics (2nd edition): Greg and his wife together had an unpaid balance of $500 on their credit cards for one month. The company that issued Greg's credit card charges interest of 2% a month on the unpaid balance; his wife's charges are 1.5% a month. If the total finance charge for both was $9.00, how much was each unpaid balance?

give me 2 equations for this problem.

Answer 1

Let "a" be the amount of unpaid balance Greg has.
Let "b" be the amount of unpaid balance Greg's wife has.
a+b=$500 --------- (statement 1)
2%a+1.5%b=$9
2a+1.5b=$900 --------- (statement 2)
2 x (statement 1) :
2a + 2b = $ 1000 ----------- (statement 3)
(statement 3) - (statement 1) :
0.5b = $100
b= $200
Substitute b=$200 into statement 1.
a+$200=$500
a=$300
Greg's unpaid balance is $300.
His wife's unpaid balance is $200.

Answer 2

Let the unpaid balance on Greg's cc be x. His wife's would be 500-x.

2/100 (x) + 1.5/100 (500-x) = 9

Just solve for x...