# Barbie is thinking of a number. Twenty less than one-third of the number is 72. What is Barbie's number?

## I know that this is an easy equation but I keep on ending up with 236 as my answer. Help? Please include work on the problem

Jan 29, 2018

$276$

#### Explanation:

Let the number be $x$

Then, $\frac{1}{3} x - 20 = 72$

or, $\frac{1}{3} x = 72 + 20$

or, $\frac{1}{3} x = 92$

or, $x = 92 \times 3$ = $276$

Jan 29, 2018

Let the number Barbie is thinking of be $x$

$\frac{x}{3} - 20 = 72$

solve for $x$

#### Explanation:

$\frac{x}{3} - 20 = 72$

$\frac{x}{3} = 92$

multiply both sides by 3

$x = 276$

Jan 29, 2018

$x = 276$

#### Explanation:

All right. Let's write an equation.

$\text{Twenty less than one-third of the number is 72}$

Using $x$ as the number, the sentence is equivalent to

$\frac{x}{3} - 20 = 72$

We add 20 on both sides.

=>$\frac{x}{3} - 20 + 20 = 72 + 20$

=>$\frac{x}{3} = 92$ We now multiply both sides by 3.

=>$\left(\frac{x}{3}\right) 3 = 92 \cdot 3$

=>$x = 276$

I think that you did something like this:

$\frac{x}{3} - 20 = 72$

$x - 20 = 216$

=>$x = 236$

This would not be true because when you multiply both sides by 3, you would get:

$3 \left(\frac{x}{3} - 20\right) = 72 \cdot 3$ Distribute.

=>$x - 60 = 216$

=>$x = 276$

We still get the same answer.

Jan 29, 2018

Barbie's number is $276$, see below:

#### Explanation:

$\frac{1}{3} \cdot x - 20 = 72$

$\frac{1}{3} \cdot x \cancel{- 20 + \textcolor{red}{20}} = 72 + \textcolor{red}{20}$

$\frac{1}{3} \cdot x = 92$

$\cancel{\frac{1}{3}} \cdot x \cdot \cancel{\textcolor{red}{3}} = 92 \textcolor{red}{\cdot 3}$

$x = 276$