Sarah’s two student loans totaled $12,000. One of her loans was at 6% simple interest and the other at 9%. After one year, Sarah owed $855 in interest. What was the amount of each loan?
Let X be one loan amount and Y the other.
X = $12,000 - Y
.06X + .09Y = $855
Substitute ($12,000 - Y) for X in the second equation and solve for Y. Put that value into the first equation to find X. Check by putting both values in the second equation.
I hope this helps. Thanks for asking.
Thank you, that help a lot. It was very clear to understand
Y= $4,500
X= $7,500
To find the amount of each loan, let's assume the loan with 6% interest is x dollars and the loan with 9% interest is y dollars.
According to the given information, the sum of the two loans is $12,000:
x + y = $12,000 --------------- (Equation 1)
The total interest after one year is $855. The interest is calculated by multiplying the loan amount by the interest rate and the time (in years):
0.06x + 0.09y = $855
To make the equations simpler, let's multiply both sides of the second equation by 100:
6x + 9y = 85500 --------------- (Equation 2)
Now, we have a system of linear equations with two variables (x and y):
x + y = 12,000
6x + 9y = 85,500
We can solve this system of equations using the method of substitution or elimination.
Let's isolate one variable in Equation 1:
x = 12,000 - y
Now substitute this value of x into Equation 2:
6(12,000 - y) + 9y = 85,500
Expand and simplify the equation:
72,000 - 6y + 9y = 85,500
3y = 13,500
y = 4,500
Now substitute the value of y back into Equation 1 to find x:
x + 4,500 = 12,000
x = 7,500
Therefore, Sarah's loan with 6% interest is $7,500, and her loan with 9% interest is $4,500.