Question

14. Yang owed two credit cards with balances of $7,500 and $3,500. The card with the $3,500 balance charged 1.4% more than the other. At the end of one year, he paid is $797. What was the simple interest of each card?

Remark: Each problem worth 3 points. There are 14 problems in total. Additional 3 points will be added if you are involved in my homework list.​​

Answer 1

Explanation:

the phrasing of the problem statement is not very precise.

the interest rate of the first card is x.

the interest rate of the second card is x + 0.014 (that is 1.4% more that the other card).

I assume that is the correct interpretation of 1.4% more.

e.g. if card 1 has an interest rate of 15%, then card 2 has an interest rate of 15 + 1.4 = 16.4%.

and I don't think that means to add 1.4% of 15% (which would be 15×1.014 = 15.21%)

remember, a n% rate is expressed as n/100.

so, 100% = 1

10% = 0.1

1% = 0.01

if I understand the problem definition correctly, he paid only interest (and no principal = balance) at the end of the year.

and the interest of an amount is that amount multiplied by the interest rate :

7500x + 3500(x + 0.014) = 797

7500x + 3500x + 49 = 797

11000x + 49 = 797

11000x = 748

x = 748/11000 = 0.068 = 6.8%

x + 0.014 = 0.082 = 8.2%

so, the first card (with $7,500) charges 6.8% interest.

the second card (with $3,500) charges 8.2% interest.