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Question 1142733: A college used a $7,000 gift from an alumnus to make two student loans. The first was at 3% annual interest to a nursing student. The second was at 6% to a business major. If the college collected $300 in interest the first year, how much was loaned to each student?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Let x = the amount loaned at 6% and y = the amount loaned at 3%.
Then from the condition you have these two equations in two unknowns
x + y = 7000 dollars (1) (total of the two loans)
0.06x + 0.03y = 300 dollars (2) (total interest)
Solve the system by the Substitution method.
For it, from equation (1) express x = 7000 - y and substitute it into equation (2). You will get
0.06*(7000-y) + 0.03y = 300
Simplify and express y from the last equation; then calculate
y =  = 4000.
To find x, substitute the found value of y into equation (1). You will get then
x = 7000 - 4000 = 3000.
ANSWER. $4000 was loaned at 3% and $3000 was loaned at 6%.
CHECK. 0.03*4000 + 0.6*3000 = 300 dollars. ! Correct !
Solved.
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It is a typical and standard problem on investment.
To see many other similar solved problems on investment, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
(1) Do the calculation to determine that $300 return on $7000 represents an interest rate of (30/7)%, or 4 2/7%.
(2) Do the calculations to determine that 4 2/7% is 3/7 of the way from 3% to 6%.
(3) That means 3/7 of the total was loaned at the higher rate.
ANSWER: 3/7 of $7000, or $3000, at 6%; the other $4000 at 3%.
CHECK: .06(3000)+.03(4000) = 180+120 = 300.
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