SOLUTION: The sum of the three smallest of four consecutive odd integers is 30 more than the largest integer. What are the four consecutive odd integers?

Question 832594: The sum of the three smallest of four consecutive odd integers is 30 more than the largest integer. What are the four consecutive odd integers?

Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!

Hi, there--

THE PROBLEM:
The sum of the three smallest of four consecutive odd integers is 30 more than the largest integer.  What are the four consecutive odd integers?

A SOLUTION:
Let x be the smallest odd integer.

Then the other three consecutive odd integers are x + 2, x + 4, and x + 5.

The sum of the smallest three integers is 30 more than the largest integer, so

x + (x + 2) + (x + 3) = (x + 5) + 30

Solve for x to find the smallest integer.

3x + 5 = x + 35
2x + 5 = 35
2x = 30
x = 15

In the context of this problem, x = 15 means that the smallest odd integer is 15. 
The other three integers are 17, 19, and 21.

Check your answer:
The sum of the three smallest odd integers is 15+17+19=51, and 51 is 30 more than 21. Check!


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com

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