Question

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?

Answer 1

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(n+3)=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:

`2n+2*3=15`
`2n+6=15`

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

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

Divide both sides by 2:

`(2n)/2 = 9/2`
`n=9/2 = 4 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.