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Chapter 3: Q15. (page 151)

What is the greatest of five consecutive integers if the sum of these integers equals 135?

Short Answer

Expert verified

The greatest of five consecutive integers, if the sum of these integers equals 135 is 29.

Step by step solution

01

– Consecutive integers

The integers that follow each other are called the consecutive integers.

That is if x is an integer, then x+1andx+2are consecutive integers.

02

– Find an equation that is used to find the greatest of five consecutive integers.

Let x be an integer.

Then the five consecutive integers will be x,x+1,x+2,x+3,and x+4.

The sum of these five consecutive integers is 135.

This can be mathematically written as follows:

x+x+1+x+2+x+3+x+4=1355x+10=135

03

– Find value of x.

Solve 5x+10=135:

5x+10=1355x=125鈥勨赌勨赌勨赌凷耻产迟谤补肠迟10蹿谤辞尘产辞迟丑蝉颈诲别蝉x=25鈥勨赌勨赌勨赌刣颈惫颈诲别产辞迟丑蝉颈诲别蝉产测5

04

– Find all the 5 consecutive integers.

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

x+3=25+3=28x+4=25+4=29

So, the 5 consecutive integers are 25, 26, 27, 28, and 29.

Hence, the greatest of five consecutive integers, if the sum of these integers equals 135 is 29.

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