|
Question 1103832: Charlie invested his savings in two investment funds. The
$4000
that he invested in Fund A returned a
2%
profit. The amount that he invested in Fund B returned a
5%
profit. How much did he invest in Fund B, if both funds together returned a
3%
profit?
Found 3 solutions by greenestamps, ikleyn, richwmiller:
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
NOTE: I misread the problem, thinking that the $4000 was the total amount invested.
Skip down to the ================= to see the revised solution.
Here, first, is the quick way to get the answer to a problem like this. We can look at the slow, formal algebraic method later.
The 3% average return is twice as close to 2% as it is to 5%. That means twice as much was invested at 2% as at 5%.
That means the $4000 was invested with 2/3 of it at 2% and 1/3 of it at 5%.
1/3 of $4000 is $1333.33 (which indicates "bad" numbers are used for this problem....)
2/3 of $4000 is $2666.67
So the amount he invested in Fund B was $1333.33.
Now the standard algebraic solution method....
"The return for x amount in Fund B at 5%, plus the return for the rest (4000-x) in Fund A at 2%, yielded an average return of 3% on the total investment".
Translated into an algebraic equation,
 [note the form for each term on both sides of the equation is the same: (interest rate)*(amount)]
 [simplify the calculation by getting rid of the decimals]
The amount invested in Fund B at 5% was $1333.33.
========================================================================
Here, first, is the quick way to get the answer to a problem like this. We can look at the slow, formal algebraic method later.
The 3% average return is twice as close to 2% as it is to 5%. That means twice as much was invested at 2% as at 5%.
Since twice as much was invested in Fund A as in Fund B, the amount he invested in Fund B was $2000.
Now the standard algebraic solution method....
"The return for x amount in Fund B at 5%, plus the return for the 4000 in Fund A at 2%, yielded an average return of 3% on the total investment".
Translated into an algebraic equation,
 [note the form for each term on both sides of the equation is the same: (interest rate)*(amount)]
 [simplify the calculation by getting rid of the decimals]
The amount invested in Fund B at 5% was $2000.
Answer by ikleyn(52817)  (Show Source):
You can put this solution on YOUR website! .
Charlie invested his savings in two investment funds.
The $4000 that he invested in Fund A returned a 2% profit.
The amount that he invested in Fund B returned a 5% profit.
How much did he invest in Fund B, if both funds together returned a 3% profit?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
interest + interest = interest
0.02*4000 + 0.05*x = 0.03*(4000+x)
80 + 0.05x = 120 + 0.03x
0.05x - 0.03x = 120 - 80
0.02x = 40 ====> x =  =  = 2000.
Answer. $2000 was invested in Fund B.
Check. 0.02*4000 + 0.05*2000 = 180 dollars;
0.03*(4000 + 2000) = 180 dollars. ! Correct !
-------------------
To see other similar problems on investment solved, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! We have 4000 dollars of 2% investment.
Using the method of alligation.
2 2 4000 dollars of 2% investment
3 6000 dollars of 3% investment
5 1 1/2*4000=2000 dollars of 5% investment
3
1= 3 - 2
2= 5 - 3
2000= 4000/(2/1) dollars of 5% investment to add to your 4000 dollars of 2% investment.
6000= (4000+2000) dollars of the final 3% investment.
check
0.05 * 2000 + 0.02 * 4000 = 0.03*(4000+2000)
100.0 + 80.0 = 0.03*(6000)
180.0 = 180.0
ok
|
|
|
| |
