Question

A student takes out two loans totaling $10,000 to help pay for college expenses. One loan is at 4% simple interest, and the other is at 9% simple interest. The first-year interest is . Find the amount of the loan at 9%.
A) $3000
B) $120
C) $630
D) $7000

Answer 1

I think we are missing the value of the first year interest. Do you have that number?

Answer 2

$750

Answer 3

We know that there are two loans. We know that the sum of the two loans is $10,000.

So let's assign a variable to each loan.
Let a= loan one
Let b=loan two

Since we have two variables, we need two equations to solve this problem.

The first equation is: loan one + loan two = $10,000 or a+b=10,000

Answer 4

We also know that the interest charge on loan one plus the interest charge on loan two is $750. So the second equation looks like this:

interest charge loan one + interest charge loan two = 750

To find out the interest charge in simple interest on each loan, we change the percent to a decimal and then multiply the decimal by the loan amount.

So for loan one, change 4% to .04. Next multiply by the loan amount, which we are using the variable a to represent. So the interest charge for loan one looks like this: .04a

Do the same thing for loan two. Change 9% to .09 decimal. Next multiply by the loan amount, which we are using variable b to represent. So the interest charge for loan two looks like this: .09b

We can now write our second equation with the variables. Our second equation looks like this:

.04a+.09b=750

Answer 5

We now have two equations. So we can solve for the two variables.

.04a+.09b=750
a+b=10,000

Rearrange the bottom equation.
a=10,000-b

Substitute into the top equation.

.04(10,000-b)+.09b=750

Distribute .04(10,000-b)

400-.04b+.09b=750

Combine like terms.

400+05b=750

rearrange the equation.

.05b=750-400

Solve for b
.05b=350
b=7,000

So the amount of the second loan is 7,000 dollars.

Answer 6

Thank you so much!