SOLUTION: Chris 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 7% profit. How much

Question 1204040: Chris 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 7% profit. How much did he invest in Fund B, if both funds together returned a 5% profit?
Found 4 solutions by ikleyn, josgarithmetic, greenestamps, MathTherapy:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Chris 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 7% profit.
How much did he invest in Fund B, if both funds together returned a 5% profit?
~~~~~~~~~~~~~~~~~~~~~

Your equation is 0.02*4000 + 0.07*B = 0.05*(4000+B) To find B, simplify it step by step 80 + 0.07B = 200 + 0.05B 0.07B - 0.05 = 200 - 80 0.02B = 120 B = 120/0.02 = 6000. ANSWER CHECK. Left side of equation (1) is 0.02*4000 + 0.07*6000 = 500. Right side is 0.05*(4000+6000) = 500, the same number. ! correct !

Solved.

-------------------

The solution by @josgarithmetic, giving the answer 2400 for amount B,
is incorrect, starting from his very first line to the very end.

No one line of his post is correct.

For the safety of your mind, you better ignore his post
as if you never seen it before.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

ACCOUNT %RATE INVESTED AMT. RETURNED A 2 4000 (0.02)(4000) B 7 b 0.07b

5% profit on invested amount 4000+b.
---------solve for b.

--------------------------seriously misread problem------below here is wrong------
A and B, amounts invested in plans A and B

A little simplifying,

Question asked for B.

E1-E2,...
AMP Parsing Error of [highlight()]: Invalid expression ')': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Tutor @josgarithmetic did not work the problem that was given....

Tutor @ikleyn provided a response showing a typical formal algebraic solution.

This problem can be viewed as a "mixture" problem, in which we are "mixing" an investment that returns a 2% profit with another that returns a 7% profit, yielding an average profit of 5%.

Here is an unorthodox informal method for solving any 2-part mixture problem like this.

Consider the three percentages (on a number line, if it helps) -- 2, 5, and 7 -- and observe/calculate that 5 is 3/5 of the way from 2 to 7.

That means 3/5 of the "mixture" is the money invested in the fund that returned the 7% profit. That "3/5" fraction means the money was invested in the two funds in the ratio 3:2, with the larger portion in the fund that returned 7% profit.

Since $4000 was invested in the fund that returned a 2% profit, the amount invested in the fund that returned 7% profit can be solved using a proportion:

ANSWER: $6000 was invested in fund B

All the words of explanation make this sound like a long process, but the actual calculations are quick and easy:

5% is 3/5 of the way from 2% to 7%
The two amounts invested are in the ratio 3:2
The smaller amount is $4000, so the larger amount is $6000

ANSWER: $6000

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Chris 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 7% profit. How much did he invest in Fund B, if both funds together returned a 5% profit? Let amount invested in Fund B, be B Amount invested in Fund A: $4,000, so profit from Fund A investment = .02(4,000) Amount invested in Fund B: B, so profit from Fund B investment = .07B Since overall profit from the 2 investments was 5%, we get the following Return on Investment (ROI) equation: .02(4,000) + .07B = .05(4,000 + B) 80 + .07B = 200 + .05B .07B - .05B = 200 - 80 .02B = 120 Amount invested in Fund B, or

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