Question

In the following exercises, solve each number word

The sum of two numbers is $-284$. One number is $62$less than the other. Find the numbers.

Short answer

The number is $-111$and the other number is $-173$.

Step-by-step solution

Step 1. Given Information  

We are given that one number is $62$less than the other and their sum is $-284$.

We have to find the numbers.

Step 2. Forming the equation   

Let the number be x,

So, the other number will be $x-62$,

So, the equation will be,

$$\begin{gathered} x+x-62=-284 \\ 2x-62=-284 \end{gathered}$$

Step 3. Solving the equation  

Adding $62$from both sides, we get

$$\begin{gathered} 2x-62=-284 \\ 2x-62+62=-284+62 \\ 2x=-222 \end{gathered}$$

Dividing by $2$,

$$\begin{gathered} x=\frac{-222}{2} \\ x=-111 \end{gathered}$$

The other number will be $-111-62=-173$,

Hence, the number is $-111$and the other number is $-173$.

Step 4. Checking the solution   

Putting the value of xin the equation, we get

$$\begin{gathered} x+x-62=-284 \\ -111-111-62=-284 \\ -284=-284 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.