Sue's student loans totaled $31,000. One of her loans was at 2.8% simple interest and the other at 4.5%. After one year, Sue owed $1024.40 in interest. What was the amount of each loan?
x = loan at 2.8%, y = loan at 4.5%
0.028x + 0.045y = 1024.40
x + y = 31000
solve these two equations together for your answer
post back if you need help
I'm not getting the result I was looking for, How do you deturmine what the amount of each interest?
Take x+y=31000 and solve for one of the variables.
Next, plug that solution into the second equation using the substitution method.
You now have a complete solution to one of the variables. Plug that answer into the original equation (x+y=31000) and you will find the solution of the second variable.
Once you have both of the solutions plug them into their separate terms. For example, if x=3 plug in that number to 0.028x
That will give you the separate value of each interest amount. Hope this helped.
Opps.. when i said Original equation, I meant 0.028x + 0.045y = 1024.40
To find the amount of each loan, let's assume the amount of the loan at 2.8% simple interest is x dollars, and the amount of the loan at 4.5% simple interest is (31000 - x) dollars.
To calculate the interest on the loan at 2.8%, we can use the formula:
Interest = Principal * Rate * Time
For the loan at 2.8%, the interest is (x * 0.028 * 1) = 0.028x.
Similarly, for the loan at 4.5%, the interest is ((31000 - x) * 0.045 * 1) = 0.045(31000 - x).
According to the problem, the total interest after one year is $1024.40. Therefore, we can write the equation:
0.028x + 0.045(31000 - x) = 1024.40
Now, let's solve this equation to find the value of x.
0.028x + 0.045(31000 - x) = 1024.40
0.028x + 1395 - 0.045x = 1024.40
-0.017x = -370.60
x = -370.60 / -0.017
x ≈ 21788.24
So, Sue's loan at 2.8% interest is approximately $21,788.24, and her loan at 4.5% interest is approximately $9,211.76.