Question

Asel's two students loan totaled $12000. One of her loan was at 3.2% simple interest rate an the other at 4.5%. after one year, Asel owed $442.50 in interest. What was the amount of each loan? Solution: $7500 at 3.2% and $4500 at 4.5%

Answer 1

To solve the problem, set up a system of equations and use substitution to find the values of x and y. The first loan is $7500 and the second loan is $4500.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the amount of the loan with a 3.2% interest rate, and let y represent the amount of the loan with a 4.5% interest rate. We have two equations:

x + y = 12000

0.032x + 0.045y = 442.50

We can solve this system of equations by substitution or elimination. Let's use substitution.

First, we can rewrite the first equation as x = 12000 - y.

Substituting this expression for x into the second equation, we have:

0.032(12000 - y) + 0.045y = 442.50

Simplifying the equation, we get:

384 - 0.032y + 0.045y = 442.50

Combining like terms, we get:

0.013y = 58.50

Dividing both sides by 0.013, we find that y ≈ 4500.

Substituting this value of y back into the first equation, we can solve for x:

x + 4500 = 12000

x = 7500

Therefore, the amount of the first loan is $7500 and the amount of the second loan is $4500.