Q15. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1 – 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.

Step 2 – 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:

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

Step 3 – Find value of x.

Solve $5x+10=135$:

$\begin{array}{c}5x+10=135\\ 5x=125\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}Subtract 10 from both sides}\\ x=25\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}divide both sides by 5}\end{array}$

Step 4 – 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.