Question

In the following exercises, solve each number word

One number is $14$less than another. If their sum is increased by seven, the result is $85$. Find the numbers.

Short answer

The number is $46$and the other number is $32$.

Step-by-step solution

Step 1. Given Information  

We are given that one number is $14$less than another.

We have to find the numbers.

Step 2. Forming the equation   

Let the number be x,

So, the other number will be $x-14$,

We know that when sum of the numbers is incresed by $7$, we get$85$

So, the equation will be,

$$\begin{gathered} x+(x-14)+7=85 \\ x+x-14+7=85 \\ 2x-7=85 \end{gathered}$$

Step 3. Solving the equation  

Adding $7$on both sides, we get

$$\begin{gathered} 2x-7=85 \\ 2x-7+7=85+7 \\ 2x=92 \end{gathered}$$

Dividing by $2$,

$$\begin{gathered} x=\frac{92}{2} \\ x=46 \end{gathered}$$

The other number will be $46-14=32$,

Hence, the number is $46$and the other number is$32$.

Step 4. Checking the solution   

Putting the value of xin the equation, we get

$$\begin{gathered} x+(x-14)+7=85 \\ 46+(46-14)+7=85 \\ 46+32+7=85 \\ 85=85 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.