Chapter 1.5, Problem 36WE

To determine

To find the first number.

Answer to Problem 36WE

First number is $\frac{124}{3}$ .

Explanation of Solution

Given information:

The sum of three numbers is 120. The second number is $8$ less than the first number and third number is $4$ more than the first number.

Calculation:

Let first number is $x$ .

Now, second number is $\left(x-8\right)$ and third number is $\left(x+4\right)$ .

Thus

  $\begin{array}{l}x+x-8+x+4=120\\ 3x-4=120\\ 3x=120+4\\ 3x=124\\ \Rightarrow x=\frac{124}{3}\end{array}$

Hence

  $\text{First number}=\frac{124}{3}$

  $\begin{array}{l}\text{Second number}=\frac{124}{3}-8\\ =\frac{124-24}{3}\\ =\frac{100}{3}\end{array}$

And

  $\begin{array}{l}\text{Third number}=\frac{124}{3}+4\\ =\frac{124+12}{3}\\ =\frac{136}{3}\end{array}$