Question

The sum of two numbers is 40. If 2 is added to the larger number, theresult is equal to twice the smaller number. What are the two numbers?

Answer 1

We have 2 numbers. We can call them x and y, being x the smaller one.

The sum of this two numbers is 40, so we can write:

`x+y=40`

We know that if 2 is added to the larger number (that we name as y), the result is twice the smaller number, that would be 2x. Then, we can express this as:

`y+2=2x`

We can express y in function of x from the second equation and then replace it in the first equation to solve for x:

`y+2=2x\Rightarrow y=2x-2`
`\begin{gathered} x+y=40 \\ x+(2x-2)=40 \\ 3x-2=40 \\ 3x=40+2 \\ 3x=42 \\ x=(42)/(3) \\ x=14 \end{gathered}`

Now, we can calculate y as:

`\begin{gathered} y=2x-2 \\ y=2(14)-2 \\ y=28-2 \\ y=26 \end{gathered}`

Answer: the two numbers are 14 and 26.