# How do you define a variable and write an expression for each phrase: one-third of the total of nine times a number and twenty one?

Jul 25, 2017

$3 x + 9$

#### Explanation:

You don't need to "define" a variable, if that is what you mean. A variable can be any letter - $x$, $r$, $d$, etc etc. But $x$ is the most common, and so I shall stick to it here.

One third of the total of states that the "nine times a number and twenty one" comes before the one-third.

Since we defined "a number" to be $x$, then nine times $x$ is simplify $9 x$.

The "total of" is telling us to take the sum of $9 x$ and $21$. It is just simplify $9 x + 21$

And then it is asking us to take $\frac{1}{3}$ of that. That is just dividing $9 x + 21$ by $3$, as $9 x + 21 \cdot \frac{1}{3} = \left(9 x + 21\right) \div \frac{3}{1}$. $9 x$ divided by $3$
is $3 x$, and $27$ divided by $3$ is $9$.

Therefore we get $3 x + 9$