SOLUTION: 1. Samantha�s student loans total $18,000. Part was a personal loan at 11% interest; the other was a Stafford loan at 7%. After one year the loans accumulated $1660 in interest.

Question 427001: 1. Samantha�s student loans total $18,000. Part was a personal loan at 11% interest; the other was a Stafford loan at 7%. After one year the loans accumulated $1660 in interest. What was the amount of each loan?
a) Develop an equation to represent the sum of the loans, use �x� for the personal loan, use �y� for the Stafford loan.
b) Develop an equation to represent the interest accumulated in the first year. Use �x� for the personal loan, use �y� for the Stafford loan.
c) Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine the amount of each loan. Show all your work from problem statement through the final result.
d) What are the intercepts of the equation from part a of this problem? Where would the lines intersect if you solved the system by graphing?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Personal Loan = $x
Stanford Loan $y

x+y= 18000 .............1
11%ofx +7%ofy = 1660
Multiply by 100
11x+7y=166,000
7y=166000-11x---------2
/7
y=23714.29-1.57x
Plug the value of y in (1)
x+(23714.29-1.57 x)=18000
x+23714.29-1.57 x=18000
x-1.57x= 18000-23714.29
-0.57x=-5714.29
/-0.57
x=10000 at 11%
Plug the value of x in (1)
x+y=18000
10000+y =18000
y=8000 at7%

RELATED QUESTIONS
Samantha�s student loans total $20,000. Part was a personal loan at 12% interest; the... (answered by stanbon)

I just can't seem to catch on to word problems - can you help? I need to have a problem... (answered by richwmiller)

A student takes out two loans, one at 5% interest and the other at 6% interest. The 5%... (answered by Maths68)

Student loans are a hot discussion topic today both in the news and at home. Those of us... (answered by solver91311)

A student takes out two loans, one at 5% interest and the other at 6% interest. The 5%... (answered by robertb)

A bank loans me $13,000 for one year. Part of the loan is at 8% Part of the loan is at... (answered by ankor@dixie-net.com)

Sarah has two student loans totaling $12,000. One of loans was @6% simple interest and... (answered by stanbon)

A company obtained two loans totaling $30,000. The interest rate for one loan was 16... (answered by mananth)

Sarah�s two student loans totaled $12,000. One of her loans was at 6% simple interest and (answered by nyc_function)