Question

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

Short answer

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

Step-by-step solution

– Consecutive integers

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

That is if x is an integer, then $x+1\text{and}x+2$are consecutive integers.

– 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:

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

– Find value of x.

Solve $5x+10=135$:

$\begin{array}{c}5x+10=135\\ 5x=125\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}Subtract10frombothsides}\\ x=25\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}dividebothsidesby5}\end{array}$

– Find all the 5 consecutive integers.

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

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

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.