Chapter 3: Q15. (page 151)

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

Expert verified

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

Step by step solution

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

That is if x is an integer, then $x + 1 and x + 2$ are 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:

$\begin{matrix} x + x + 1 + x + 2 + x + 3 + x + 4 = 135 \\ 5 x + 10 = 135 \end{matrix}$

Solve $5 x + 10 = 135$ :

$\begin{matrix} 5 x + 10 = 135 \\ 5 x = 125 Subtract10frombothsides \\ x = 25 dividebothsidesby5 \end{matrix}$

$\begin{matrix} x = 25 \\ x + 1 = 25 + 1 \\ = 26 \\ x + 2 = 25 + 2 \\ = 27 \end{matrix}$

$\begin{matrix} x + 3 = 25 + 3 \\ = 28 \\ x + 4 = 25 + 4 \\ = 29 \end{matrix}$

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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