|
Question 1142098: an investor invested a total of $1,800 in two mutual funds. One fund earned a 6% profit while the other earned a 3% profit. If the investor's profit was $69, how much was invested in each mutual fund?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount at 6%, in dollars.
Then the amount at 3% is the rest (1800-x) dollars.
The interest from the 6% amount is 0.06*x dollars.
The interest from the 3% amount is 0.03*(1800-x) dollars.
Your equation is
interest + interest = total interest, or
0.06*x + 0.03*(1800-x) = 69 dollars.
From the equation, express x and calculate the answer
x =  = 500.
Answer. The amount at 6% is $500; the rest $1800-$500 = $1300 is the amount at 3%.
Check. 0.06*500 + 0.03*1300 = 69 dollars. ! Correct !
-----------------
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(13196)  (Show Source):
You can put this solution on YOUR website! Here is a non-algebraic method for solving mixture problems like this that can get you to the answer much faster than the traditional algebraic method if you understand how to use it (and if an algebraic solution is not required).
(1) Determine the amounts of interest if the entire $1800 were invested at 3% and at 6%.
1800*.03 = 54
1800*,06 = 108
(2) Consider the three interest amounts on a number line -- 54, 69, and 108.
(3) Find what fraction of the way from 54 to 108 the number 69 is.
108-54 = 54; 69-54 = 15.
69 is 15/54 = 5/18 of the way from 54 to 108.
(4) That fraction is the fraction of the mixture that is at the higher rate.
ANSWER: 5/18 of $1800 = $500 at 6%; the rest, $1300, at 3%.
|
|
|
| |
