Solve Investment Problem: Net Profit $1,850 from $13,500 Bonus

[Kos46]

Hello,
Could someone please help me with the problem I've typed below? It is very similar to another problem on this forum <http://mathhelpboards.com/pre-algebra-algebra-2/investment-problem-8808.html>. I've tried to solve it in a similar way (exclusion and/or substitution) but I keep getting the values \$19 916.67 (fund) and -\$6416.67 (stock) for my answer, which obviously can't be right. I would really appreciate it if someone could tell me how to solve this the right way.

Here is my problem:
Jerome invested part of his \$13,500 bonus in a fund that paid an 8% profit and
invested the rest in stock that lost 4%. What was his investment in the fund if
his overall net profit was \$1,850?

Thank you for any help at all!
Judith

 

[MarkFL]

I would let $F$ be the amount invested in the fund and $S$ be the amount invested in the stock. So, right away we know:

\(\displaystyle F+S=13500\tag{1}\)
And then the information regarding the profit may be written as:

\(\displaystyle 0.08F-0.04S=1850\tag{2}\)
So, since we're asked to find $F$, solve (1) for $S$, substitute this into (2), and then solve for $F$. :)

 

[Kos46]

I would let $F$ be the amount invested in the fund and $S$ be the amount invested in the stock. So, right away we know:

\(\displaystyle F+S=13500\tag{1}\)
And then the information regarding the profit may be written as:

\(\displaystyle 0.08F-0.04S=1850\tag{2}\)
So, since we're asked to find $F$, solve (1) for $S$, substitute this into (2), and then solve for $F$. :)

Wow! Thank you for replying so quickly!
OK, so, I have
Let x = the amount of money that made an 8% profit
Let y = the amount of money that lost 4%

[1] x + y = 13 500
x = 13 500 - y
y = 13 500 -x

[2] 8/100x - 4/100y = 1850
Multiply both sides by 100 to get rid of fractions
8x - 4y = 185000
8x - 4(13500 - x) = 185000
8x - 54000 + 4x = 185000
12x = 239000
x = 19916.67
Therefore, y = -6416.67 ?

Or by elimination
[1] x + y = 13500
[2] 8x - 4y = 185000

So, multiply [1] by 4 so that y cancels out:

[1] 4x + 4y = 54000
[2] 8x - 4y = 185000
12x = 239000
x = 19916.67

:( If you have time, could you please tell me what I'm doing wrong here?

 

[MarkFL]

I think the issue here is not with your work, but with the problem instead. If Jerome had invested his entire bonus in the stock, his net profit would be less than \$1850, it would only be \$1080. This is why you're getting answers that don't make sense. :)

 

[Kos46]

Thank you so much for confirming my suspicions that the question was flawed! I can't tell you how many times I've tried to solve it. :)

 

[Wilmer]

If the givens in the problem are correct, then the problem
should state the period of time over which this resulted;
it is certainly not 1 year, as Mark clearly shows.

I fiddled around with this mystery.
Assuming 9000 @ 8%, thus 4500 @ -4%,
then 1850 would be correct IF time = ~3.426 years.

9000(.08)(3.426) = 2466.72
4500(-.04)(3.426)=-616.68
for net of 1850.04

Amen.

Howz things in St-Augustine Mark?