story problem

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 1 year, then how much
did she invest in each fund?
$50,000 - $20,000 = $30,000
a = $30,000 - b
0.16a + 0.25b = $6060


I am unsure of what to do next or is the problem unsolvable and an equation? Sorry, I am confused.

mauigirl300 said:

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 1 year, then how much
did she invest in each fund?
$50,000 - $20,000 = $30,000
a = $30,000 - b
0.16a + 0.25b = $6060


I am unsure of what to do next or is the problem unsolvable and an equation? Sorry, I am confused.

Click to expand...

What you've done so far looks good to me.

BUT...you did not define your variables!!!

Is
a = amount invested in Dreyfus fund?

Is b = amount invested in Templeton fund??

If that's how you defined your variables, then MAYBE you are ok...

Please let us know what you were thinking.

You are correct in your assumption regarding variable a and b.

mauigirl300 said:

a = $30,000 - b
0.16a + 0.25b = $6060
I am unsure of what to do next or is the problem unsolvable and an equation? Sorry, I am confused.

Click to expand...

Hint : if the number of variables is the same as the number of equations, you can *usually* find a solution.

I'll suggest two ways...

1)

You've worked out a = 30000-b. You could substitute this into the other equation, to get 0.16(30000-b)+0.25b = 6060. This (when simplified) will be a single equation for b, which you can solve. Then, this b can be substitute back into your equation for a.

2)

I think this will be easier : multiply the second equation by 4, to get 24240 = 0.64a + b. Then, add this to a = 30000-b to get 24240 + a = 0.64a + b + 30000 - b. The b's all cancel out, and you have an equation for a. Once you've solved for a, you substitute your answer into either of the original equations to find b.

No matter what (correct) method you use, if you don't make mistakes, you'll get the same answer.