story problem

Question

The sum of three consecutive odd numbers is one hundred five. What is the smallest of the three numbers?

Answer 1

Good Evening, Kristine,

Okay, let's solve the problem as follows: 

First number = 2x -1 
Second number = 2x + 1
Third number = 2x + 3 

Now, the sum of the above three expressions must equal 105, right? 

Therefore:

2x -1 + 2x + 1 +2x + 3 = 105   

Now, let's solve for x, okay? 

2x - 1 + 2x + 1 + 2x + 3 = 105 

6x + 3 = 105 

6x = 102 

x = 17



Now we need to substitute 17 for x in our expressions, right? 

2x -1 = 2 (17) - 1 = 33 <---the first number

2x + 1 = 2 (17) + 1 = 35 <---the second number

2x + 3 = 2 (17) + 3 = 37 <---the third number

Therefore, the smallest of the three numbers is 33.

Checking our work, we need to add all of the numbers to ensure they add up to 105, right? 

33 + 35 + 37 = 105 Check

I hope this solution assists you and that you have a great day tomorrow at school. If you want to leave feedback to this answer, or ask additional questions regarding the solution, please do so in the comment section located directly beneath this solution. If you need further assistance please feel free to contact any tutor. 

Answer 2

x + x+2 + x+4 = 105

 

3x + 6 = 105

 

3x = 99

 

x=33

 

33, 35, and 37