QuestionEight times a number, $x$ , equals one-third of the sum of the number and two. Which equation represents this? $8 x=\frac{1}{3}(x+2)$

Studdy Solution

STEP 1

Assumptions1. The problem involves an unknown number, represented by $x$ . . Eight times this number is equal to one-third the sum of the number and two.

STEP 2

We need to translate the given English statement into a mathematical equation. The statement says "Eight times a number, $x$ , is one-third the sum of the number and two." This can be translated as $8x = \frac{1}{}(x +2)$

STEP 3

Now, let's compare this equation with the given options to find the correct representation.
Option1 $8x + \frac{1}{3}(x +2)$ This is not correct as it adds $8x$ and $\frac{1}{3}(x +2)$ , but we need an equation where $8x$ is equal to $\frac{1}{3}(x +2)$ .
Option2 $8x = \frac{1}{3}(x +2)$ This is the correct representation as it matches with our translated equation.
Option3 $8x = \frac{1}{3}x +2$ This is not correct as it represents $8x$ as equal to $\frac{1}{3}x +2$ , not $\frac{1}{3}(x +2)$ .
Option $8x + \frac{1}{3}x +2$ This is not correct as it adds $8x$ , $\frac{1}{3}x$ , and $2$ together, but we need an equation where $8x$ is equal to $\frac{1}{3}(x +2)$ .
So, the correct representation of the situation is $8x = \frac{1}{3}(x +2)$ .

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