Question

In the following exercises, solve each number word

The sum of two numbers is $-45$. One number is nine more than the other. Find the numbers.

Short answer

The number is $-27$and the other number is $-18$.

Step-by-step solution

Step 1. Given Information  

We are given that one number is nine more than the other and their sum is $-45$.

We have to find the numbers.

Step 2. Forming the equation   

Let the number be x,

So, the other number will be $x+9$,

So, the equation will be,

$$\begin{gathered} x+\left(x+9\right)=-45 \\ 2x+9=-45 \end{gathered}$$

Step 3. Solving the equation  

Subtracting$9$on both sides, we get

$$\begin{gathered} 2x+9=-45 \\ 2x+9-9=-45-9 \\ 2x=-54 \end{gathered}$$

Dividing by $2$,

$$\begin{gathered} x=\frac{-54}{2} \\ x=-27 \end{gathered}$$

The other number will be $-27+9=-18$,

Hence, the number is $-27$and the other number is $-18$.

Step 4. Checking the solution   

Putting the value of xin the equation, we get

$$\begin{gathered} x+x+9=-45 \\ -27-27+9=-45 \\ -45=-45 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.