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%
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-> 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
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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(52794) (Show Source):
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.
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).
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