Question

A positive real number is 2 less than another. if the sum is 16, find the numbers .

Answer 1

The numbers are 7 and 9

Step-by-step explanation

Let the number be represeted by n and m.

One of these numbers (let's say n) is 2 less than the other: n = m - 2

The sum of the numbers is 16: n + m = 16

We have a system of equations:

`\begin{cases}n=m-2 \\ n+m=16\end{cases}`

We can substitute the first equation into the second and solve for m:

`\begin{gathered} (m-2)+m=16 \\ m+m-2=16 \\ 2m-2=16 \\ 2m=16+2 \\ 2m=18 \\ m=(18)/(2) \\ m=9 \end{gathered}`

And then substitute back into the first equation to find n:

`\begin{gathered} n=9-2 \\ n=7 \end{gathered}`

The numbers are 9 and 7.