SOLUTION: Find four consecutive integers such that the sum of the first and third integer is 60.

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Question 1168267: Find four consecutive integers such that the sum of the first and third integer is 60.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find four consecutive integers such that the sum of the first and third integer is 60.
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Use n, n+1, n+2 and n+3
n + n+2 = 60

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(Corrected response; I read EVEN integers originally....)

(1) Using formal algebra (slow; but you should now how to do it....)

x = 1st number
x+1 = 2nd
x+2 = 3rd
x+3 = 4th

The sum of the 1st and 3rd is 60:

x%2B%28x%2B2%29+=+60

Solve for x using basic algebra; then answer the question.

(2) Using logical reasoning and simple mental arithmetic (fast -- and the THINKING is good brain exercise)

In this sequence of consecutive integers (as in ANY arithmetic sequence), any number in the sequence is the average of the two numbers on either side.

Since in this problem the sum of the first and third numbers is 60, that means the second number is 30.

From there it takes little thinking at all to find the answer: 29, 30, 31, and 32.