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Chapter 2: Q16. (page 110)

Write an equation and solve each problem. (Lesson2.3)

Find four consecutive integers with a sum of 106.

Short Answer

Expert verified

Four consecutive numbers are 25, 26, 27, and 28.

Step by step solution

01

Step 1. Given Statement.

To find four consecutive integers with a sum of 106.

02

Step 2. Consecutive integers.

Consecutive integers can be written in the form as: x,x+1,x+2,x+3,x+4, and so on where x is any integer.

03

Step 3. Description of step.

In order to solve the problem, i.e. to find the four consecutive integers with sum of 106, take one number as x, then other three must be x+1,x+2,x+3.

Now, as given sum of these four consecutive integers is 106

Thus,

x+x+1+x+2+x+3=106x+x+1+x+2+x+3=1064x+6=1064x=106鈭�6鈬�4x=100鈬�x=1004鈬�x=25

Thus, value of x is 25 and other numbers are

x+1=25+1=26x+2=25+2=27x+3=25+3=28

Therefore, required four consecutive numbers are 25, 26, 27, and 28.

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