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#### rdf1212

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If Fran invests \$8200 at 6% per year, how much additional money must she invest at 8% to ensure that the interest she receives each year is 7% of the total investment? Write an equation, solve it, and remember to define your valuables.

I can't figure out this problem.. Can someone help please #### millsryno

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\$8200 @ 6% and \$8200 @ 8% is going to equal a total return of 7%

#### rdf1212

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well I have to put it into an equation.. Could you possibly help? Have a test tomorrow and can't figure this one out.

#### millsryno

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Dang...it's been a long ass time since I have done this...

Wouldn't it be:

1.06x + 1.08y = 1.07(x+y)
x = \$8200

I could be off on that...it's been a looooooooong time.

#### CrazyArcher

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how is the interest calculated? Monthly, yearly or compounded daily?

#### CatFishKing

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The easiest way I can see is

8200(.06) + 8200(.08) = .07x
Multiply each side by 100 to get rid of your decimals and end up with

8200(6) + 8200(8) = 7x
492 + 656 = 7x
1148 = 7x
Divide by 7 to get rid of the variable in x
x = 164
8200 + 492 = 6%
8200 + 656 = 8%
8200 + 492 + 164 = 7%
8200 + 656 - 164 = 7%

Hope this helps

#### rdf1212

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thank you that does. I really hope I can figure the one out on the test! Only one I can't do.

#### BassTrix

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The easiest way I can see is

8200(.06) + 8200(.08) = .07x
Multiply each side by 100 to get rid of your decimals and end up with

8200(6) + 8200(8) = 7x
492 + 656 = 7x
1148 = 7x
Divide by 7 to get rid of the variable in x
x = 164
8200 + 492 = 6%
8200 + 656 = 8%
8200 + 492 + 164 = 7%
8200 + 656 - 164 = 7%

Hope this helps
This is actually using more info than the original problem gives and in the equation above, X is the total amount invested, not the additional amount as asked in the problem statement.

The equation millsryno put up is correct, but this student may not be working with 2 variables just yet so replace x or y with 8200.

As a single variable equation it looks like this:

8200*.06 + X*.08 = (8200+X)*.07

Solve for X

X*.08 - X*.07 = 8200*.07 - 8200*.06

Work this out and you get X = 8200

So the answer is, you have to invest an additional \$8200 at 8% in order to get an average of 7% on the entire amount invested.

#### CatFishKing

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This is actually using more info than the original problem gives and in the equation above, X is the total amount invested, not the additional amount as asked in the problem statement.

The equation millsryno put up is correct, but this student may not be working with 2 variables just yet so replace x or y with 8200.

As a single variable equation it looks like this:

8200*.06 + X*.08 = (8200+X)*.07

Solve for X

X*.08 - X*.07 = 8200*.07 - 8200*.06

Work this out and you get X = 8200

So the answer is, you have to invest an additional \$8200 at 8% in order to get an average of 7% on the entire amount invested.
That's what it was I was beating my head on how to write it out since I already knew the answer. But I couldn't put two and two together.

#### Gonzo8879

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Does anyone else feel really stupid.... lol

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:shock:

#### Just J

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Does anyone else feel really stupid.... lol

LMFAO :Iconrotfl count me in on that.

#### rdf1212

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ahh man! I put catfish's answer down on my test.. So hopefully I get atleast partial credit

#### Obewan

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Nice BT, I kept trying to break it down with two variables, but was sure this was overkill and it was a single variable. I even had the intermediate algebra book open and found that coin problem that was posted a couple weeks ago in Chapter 5. of my book. The one were you had so many quarters, dimes and nickles that equal \$3.80. Good stuff.

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