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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%
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