Chapter 1, Problem 35CR

To determine

What are the two integers.

Answer to Problem 35CR

  $\begin{array}{l}\text{first}\text{even integer is 74}\\ \text{second even integer is 76}\end{array}$

Explanation of Solution

Given information:

The sum of two consecutive even integers is 150.

CONCEPT USED:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the two integers,

let 2x be the first even integer and 2x+2 be the second integer, then the according to the given statement adding both integer and solving them as shown below:

  $\begin{array}{l}\text{let first}\text{even integer is 2}x\\ \text{let second even integer is 2}x+2\\ 2x+2x+2=150\\ 4x+2=150\\ 4x+2-2=150-2\\ 4x=148\\ \frac{4x}{4}=\frac{148}{4}\\ x=37\\ \text{first even integer is}\\ \text{2}x=2\left(37\right)=74\\ \sec \text{ond even integers is}\\ \text{2}x+2=2\left(37\right)+2=76\end{array}$

So, the even integers are 74 and 76.