Question

One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

Short answer

If one number is nine less than another. Their sum is negative twenty-seven then the numbers are $-9\&-18$.

Step-by-step solution

Step 1. Given information  

The second number is nine less than the first number.

The sum of the first number and the second number is negative twenty-seven.

Step 2. Solution 

Consider the first number is n

One number is nine less than another.

so the second number is $n-9$

The sum of the first number and the second number is $-27$

localid="1647199414829" $$\begin{gathered} n+(n-9)=-27 \\ 2n-9=-27 \\ 2n=-18 \\ n=-9 \end{gathered}$$

So the first number is$-9$

The second number is

localid="1647199448374" $$\begin{gathered} n-9=-9-9 \\ =-18 \end{gathered}$$

So numbers arelocalid="1647199467873" $-9\&-18$.

Step 3. Verification  

$-18$is $9$less than $-9$.

$$\begin{gathered} -18=-9-9 \\ -18=-18 \end{gathered}$$

The left-hand side is equal to the right-hand side

The sum of the $-9$and $-18$is $-27$

$$\begin{gathered} (-9)+(-18)\stackrel{?}{=}-27 \\ -9-18\stackrel{?}{=}-27 \\ -27=-27 \end{gathered}$$

The left-hand side is equal to the right-hand side

So our answer is correct the numbers are $-9\&-18$.