SOLUTION: Maya invested her savings in two investment funds. The $4000 that she invested in Fund A returned a 10% profit. The amount that she invested in Fund B returned a 3% pro

Question 1122870: Maya invested her savings in two investment funds. The
$4000
that she invested in Fund A returned a
10%
profit. The amount that she invested in Fund B returned a
3%
profit. How much did she invest in Fund B, if both funds together returned a
5%
profit?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Let x = amount she invested in Fund B, in dollars (the value under the question). The interest from Fund A is 0.1*4000 dollars. The interest from Fund B is 0.03*x dollars. Total interest is 0.05*(4000+x). Your equation is interest + interest = total interest, or 0.1*4000 + 0.03*x = 0.05*(4000+x) dollars. 400 + 0.03x = 200 + 0.05x 400 - 200 = 0.05x - 0.03x 200 = 0.02x ====> x = = 10000. Answer. $10000 were invested in Fund B. Check. 0.1*4000 + 0.03*10000 = 700 dollars. 0.05*(4000+10000) = 700 dollars. ! Correct !

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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!

Algebraically....

Let x be the amount invested at 3%. Then

You can do the algebra to get the answer.

If an algebraic solution is not required, here is a much faster way to solve a problem like this.

The ratio between the amounts invested in the two places exactly determines where the overall percentage return lies between the two individual percentages.

The 5% return is 5% away from 10% and 2% away from 3%. That ratio 5:2 means the money must be split in the ratio 5:2. And since the overall return is close to 3% than to 10%, the larger amount needs to be invested at 3%.

So if x is the amount invested at 3%, we have a proportion:

or

She invested $10000 in investment B.

CHECK:

10% of $4000 = $400
3% of $10000 = $300
Total $400+$300 = $700

5% of $14000 = $700

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