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

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Question 832570: The sum of the three smallest of four consecutive integers is 30 more than the largest integer. What are the four consecutive integers?
Answer by math-vortex(648) About Me  (Show Source):
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Hi, there--

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

A SOLUTION:
Let x be the smallest integer.

Then the other three consecutive integers are x + 1, x + 2, and x+3.

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

x + (x + 1) + (x + 2) = (x + 3) + 30

Solve for x to find the smallest integer.

3x + 3 = x + 33
2x + 3 = 33
2x = 30
x = 15

In the context of this problem, x = 15 means that the smallest integer is 15. 
The other three integers are 16, 17, and 18.

Check your answer:
The sum of the three smallest integers is 15+16+17=48, and 48 is 30 more than 18. 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