# Thread: Middle School Algebra 1

1. ## Middle School Algebra 1

Okay... I'm in some desperate need of help.

This word problem:
Part of $20,000 is invested at 12% interest. The rest is invested at 8% interest. The total interest from the two accounts os$1800. How much money was invested at each rate?

Also, it would be nice to have the equation. Step by step, if I have the first one i feel i can figure the rest out. With explanations, please.

2. You have .12 and .08, the two percentage interests. You also know that at the end you get 1800 from your starting 20,000. One part, let's call it x, is put at .12 interest. The other part is put at .08 interest. We know this part is whatever we didn't put into x, so it is 20,000-x. Write this all out

.12(x) + .08(20,000-x) = 1800. Clear the decimals.
12x +8(20,000-x) = 180,000 Multiply out
12x + 160,000 -8x = 180,000 Combine the terms
4x = 20,000. Divide by 4
x = 5,000.

So you put 5,000 at 12% interest, and (20,000-5,000)= 15,000 at 8% interest.

3. Hello, Auburn!

Part of $20,000 is invested at 12% interest. The rest is invested at 8% interest. The total interest from the two accounts is$1800.
How much money was invested at each rate?
We can "talk" our way through this . . .

Let $x$ = amount invested at 12%.

Then "the rest" is $(20,\!000-x)$ dollars.

$x$ dollars at 12% earns $0.12x$ dollars in interest.

$(20,\!000-x)$ dollars at 8% earns $0.08(20,\!000-x)$ dollars in interest.

. . So the total interest is: . $0.12x + 0.08(20,\!000-x)$ dollars.

But we are told: the total interest is \$1800.

There is our equation! . . . . ${\color{blue}0.12x + 0.08(20,\!000-x) \;=\;1800}$

I recommend multiplying by 100:

. . $12x + 8(20,\!000-x) \:=\:180,\!000$

- . $12x + 160,\!000 - 8x \:=\:180,\!000$

. . . . . . . . . . . . $4x \:=\:20,\!000$

. . . . . . . . . . . . . $x \:=\:5,\!000$

Therefore: . $\begin{array}{c}\\text{5,000 was invested at 12\%} \\
\\text{15,000 was invested at 8\%}
\end{array}$

4. Ahh thank you both.

My mistake was, I had it be 20000-x) times .12 + x times .08 = 21800

Found out what i did wrong, corrected, thank you both kindly