Sarah's two student loans totaled $12,000. One of her loans was at 6% simple interest and the other at 3%. After one year, Sarah owed $585 in interest. What was the amount of each loan?

The loans are $4500 and $7500 respectively

Step-by-step explanation:

Let the principal amount of the two loans be x and y respectively.

This means x + y = 12,000 (I)

Now, for the first principal x, interest accrued will be

I = PRT/100

I = x * 6 * 1/100 = 6x/100

For the second principal, interest accrued will be;

I = y * 3 * 1/100 = 3y/100

Since the total interest is $585

That would be;

6x/100 + 3y/100 = 585

6x + 3y = 58500 (ii)

Now we have two equations to solve simultaneously.

Substitute x = 12,000 - y in equation ii

6(12000- y) + 3y = 58,500

72000 - 6y + 3y = 58500

3y = 72000 - 58500

3y = 13,500

y = 13,500/3 = 4,500

x = 12,000 - y = 12000 - 4500 = 7,500

Hence the loan at 6% is 7,500 while the loan at 3% is 4,500