How to solve a word problem

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cgarcia71

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Mar 18, 2006
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I have this word problem and am stuck.

High Risk Funds

Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in one year, then how much did she invest in each fund?

Ok so

I know that the interest rate for one fund was .16 and .25 for the other but I don't know how much was invested in each.

.16x + .25x = 6060

.41 = 6060

.41/.41 = 6060/.41

Is this correct logic?
 
Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in one year, then how much did she invest in each fund?

Ok so

I know that the interest rate for one fund was .16 and .25 for the other but I don't know how much was invested in each.

.16x + .25x = 6060
Click to expand...


Good attempt, but we need a small change. You need two variables in stead of just one. Let x be the amount invested in Dreyfus and y be the amount in Templeton. Your equation then reads

.16x + .25y = 6060

Now we have one eqn but two unknowns, so we need another ewn with those variables. We know how much money was started with:

50,000 – 20,000 = 30,000

So that must be what x and y equal:

x+ y = 30,000

Now that you have two eqns and two unknowns (a system of equations), can you solve it?
 
I did it this way not sure if it is right
0.16x + 0.25 (30,000 – x) = 6,060
0.16x + 7,500 – 0.25x = 6,060
-0.09 + 7,500 = 6,060
7,500 – 0.09 = 6,060
7,500 – 7,500 – 0.09 = -7,500 – 6,060
-0.09x = -1,440
-0.09/-0.09 x = -1,440/-0.09
X = 16,000

30,000 – 16,000 = 14,000

So

$16,000 was invested in Dreyfus New Leaders Fund and
$14,000 was invested in Templeton Growth Fund
 
suckatmath71 said:
I did it this way not sure if it is right
0.16x + 0.25 (30,000 – x) = 6,060
0.16x + 7,500 – 0.25x = 6,060
Click to expand...
Good to there. Then something went horribly wrong.

Where did the 'x' go?
7,500 – 0.09x = 6,060

How did 6060 turn negative?
-0.09x = 6,060-7500

And yet, somehow, you managed to get x = 16000.

Do me two favors:
1) Be MUCH more careful with your notation. It is not useless. Clean notation WILL save you.
2) Change your screen name. Why would anyone help anyone with an attitude like that? You're fine. Let's step it up a bit.
 
You are right...that wasn't the best choice of screen names. I have submitted a request to change it. Didn't mean anything bad by it, but I guess it displays a negative attitude.

You asked where did the 'x'? I am not sure what you mean.

Also you ask how did the 6,060 become negative. I don't see where I show it as negative. I am a little confused.
 
suckatmath71 said:
You asked where did the 'x'? I am not sure what you mean.
Click to expand...
The tutor said that you were fine up through the line quoted, and then something happened to the variable; it disappeared. So the tutor is asking "what did you do in this line, after the line I quoted, to get something that had no variable in it?"

suckatmath71 said:
Also you ask how did the 6,060 become negative. I don't see where I show it as negative.
Click to expand...
In one line, you have "= 6,060". In the next line, after having subtracted on both sides by 7,500, you have "= -7,500 - 6,060". The "minus" sign in front of the "6,060" indicates a negative; you switched, in one line, from "= +6060" to, in the next line, "= -7500 - 6060". The tutor was asking how.

Please reply with specifics.

Thank you.

Eliz.
 
ok I see now what the tutor was talking about. This is how I think the problem should look.

0.16x + 0.25 (30,000 – x) = 6,060
0.16x + 7,500 – 0.25x = 6,060
-0.09x + 7,500 = 6,060
7,500 – 0.09x = 6,060
7,500 – 7,500 – 0.09x = -7,500 + 6,060
-0.09x = -1,440
-0.09x/-0.09 = -1,440/-0.09
X = 16,000

30,000 – 16,000 = 14,000

So

$16,000 was invested in Dreyfus New Leaders Fund and
$14,000 was invested in Templeton Growth Fund


Is this correct?
 
YES, as TK said, 'twas a thing of beauty :shock:

Suppose your problem went from:
Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in one year, then how much did she invest in each fund?

to this slightly different version:
Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested $16,000 in Dreyfus New Leaders Fund with an annual yield of 16% and $14,000 in Templeton Growth Fund with an annual yield of p%. If she made $6060 on these investments in one year, then what is p% ?

Of course, p% = 25%, but can you show us how you'd calculate it?
Let's have another thing of beauty from you :wink:
 
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