Question

The product of seven and a number, increased by three, is equal to twice the number, subtracted from 39. Find the number

Answer 1

It is given that the product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.

It is required to find the number.

To do this, write the statement as an algebraic statement.

Let the number be x.

The product of 7 and a number is:

`7x`

The product of 7 and a number increased by 3 is:

`7x+3`

Twice the number is:

`2x`

Twice the number subtracted from 39 is:

`39-2x`

Since it is given that these expressions are equal, it follows that:

`7x+3=39-2x`

Solve the resulting equation for x:

`\begin{gathered} \text{ Collect like terms:} \\ \Rightarrow7x+2x=39-3 \\ \Rightarrow9x=36 \\ \text{ Divide both sides by }9: \\ \Rightarrow(9x)/(9)=(36)/(9) \\ \Rightarrow x=4 \end{gathered}`

The number is 4.