Q7. - Algebra 2

Question

The sum of three consecutive integers is 135. State what is the greatest of the three integers.

 

A. 43                                 B. 44

 

C. 45                                   D. 46

Step-by-Step Solution

Answer

The greatest of the three integer is 46 and the correct option is D.

Step 1 - State the definition of a variable.

A variable is a term that is used to represent an unknown value.

Let x be the smallest integer.

Step 2 - Obtain the integers.

Since the three integers are consecutive that one after the other, then the integers are,

x, $x+1$ and $x+2$.

The sum of these three integers is 135.

Then,

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

Simplify the equation using subtarction and division,

$\begin{array}{c}3x+3-3=135-3\\ 3x=132\\ \frac{3x}{3}=\frac{132}{3}\\ x=44\end{array}$

The other two integers are

 $\begin{array}{c}x+1=44+1\\ =45\end{array}$

And

 $\begin{array}{c}x+2=44+2\\ =46\end{array}$

 Thus the three integers are 44, 45 and 46. The greatest among the three is 46.

Step 3 - State the conclusion.

The greatest of the three integer is 46. Therefore, option D is correct.