# 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?

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.