Algebra 2 polynomial word problem

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Wed Feb 26, 2014 2:23 pm
NicoleBri says...

Terry invests \$1500 in two mutual funds. The first year, one fund grows 3.8 percent and the other grows 6 percent. Write a polynomial to represent the amount Terry's \$1500 grows to in that year if X represents the amount he invested in the fund with the lesser growth rate.
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Sat Mar 15, 2014 10:45 pm
Kale says...

It's probably too late to help you with this particular problem, but I can give you tips on how to parse word problems in general!

It's always a good idea to break down the information as much as possible and assign any needed variables. For example, we're told that:

1) \$1500 is split into two funds
2a) one fund grows by 3.8%
2b) we're told to set this to X, since it has the smaller growth rate
3) the other fund grows by 6%

We know from basic math that:

1) the fund at 6% has to be the difference between the original amount and X, or 1500 - X
2) when you have a percent increase, it's basically 100% of the original PLUS the increase, or 100% + 3.8% = 103.8% increase for X
3) percentages can be represented as decimals, so 1 + 0.038 = 1.038
4) percent increases MULTIPLIED BY the original amount get you the final amount, or X(1 + 0.038)

Putting it all together, we get:

X(1 + 0.038) + (1500 - X)(1 + 0.06) = Total Growth

Now, this only works if we're looking at just one year. Since the problem doesn't specify how many years it takes, we have to modify things a little.

You should have an idea of which form gets you the appropriate answer, so it's just a matter of taking the pieces and fitting them into that form. :)

(Hint: this problem deals with interest, so it's one of the interest formulas.)
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