The sum of three consecutive numbers is 72. What are the smallest of these numbers?
The Correct Answer and Explanation is:
Let’s break this down step by step.
We know that the sum of three consecutive numbers is 72. Let’s call the smallest of these numbers xxx. The next two consecutive numbers will be x+1x + 1x+1 and x+2x + 2x+2, respectively.
So, the sum of these three numbers is: x+(x+1)+(x+2)=72x + (x + 1) + (x + 2) = 72x+(x+1)+(x+2)=72
Now, let’s simplify the equation: x+x+1+x+2=72x + x + 1 + x + 2 = 72x+x+1+x+2=72 3x+3=723x + 3 = 723x+3=72
Next, subtract 3 from both sides to isolate the term with xxx: 3x=72−33x = 72 – 33x=72−3 3x=693x = 693x=69
Now, divide both sides by 3 to solve for xxx: x=693=23x = \frac{69}{3} = 23x=369=23
Thus, the smallest of the three consecutive numbers is 23.
To verify the solution, let’s check the three consecutive numbers: 23, 24, and 25. Adding these together: 23+24+25=7223 + 24 + 25 = 7223+24+25=72
Since the sum is correct, our solution is verified. Therefore, the smallest of the three consecutive numbers is 23.
In summary, we used algebra to express the relationship between the consecutive numbers and solved the equation step by step to find the smallest number. This method ensures accuracy and clarity in determining the answer.
