# How do you translate the following statement "Twice the total of a number and three is fifteen" into an algebraic expression and then find the number?

##### 1 Answer
Jan 31, 2016

Take the sentence and turn it into an equation, then solve it to find that $n = 4.5$.

#### Explanation:

Let's call the unknown number 'n'.

The first thing we read in the sentence is 'twice' so that means 2 times something:

2(?)=?

Next we read 'the total of a number and three'. That means to add 3 to the unknown number, 'n', that we're looking for. We'll put that in the brackets:

2(n+3) = ?

Finally, we read 'is fifteen'. That's short for 'is equal to fifteen', so we'll add that to our equation:

$2 \left(n + 3\right) = 15$

Right, we've taken all the information in the sentence and turned it into an equation. Now we just need to solve it to find the value of 'n'.

Multiply out the brackets - 2 times each thing inside the brackets:

$2 n + 2 \cdot 3 = 15$
$2 n + 6 = 15$

Subtract 6 from both sides (we're trying to get 'n' by itself)

$2 n + 6 - 6 = 15 - 6$
$2 n = 9$

Divide both sides by 2:

$\frac{2 n}{2} = \frac{9}{2}$
$n = \frac{9}{2} = 4 \frac{1}{2} = 4.5$

Checking that our answer makes sense: the total of n and 3 is 7.5, and twice 7.5 is 15.