SOLUTION: find all sets of four consecutive integers whose sum is between 16 and 24

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Question 253323: find all sets of four consecutive integers whose sum is between 16 and 24
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
16 x=3 and x=4
3456
4567

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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

16%3C+x+%2B+%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%3C24

16%3C+x+%2B+x%2B1%2Bx%2B2%2Bx%2B3%3C24

16%3C4x+%2B+6%3C24

Subtract 6 from all three sides

10%3C4x%3C18

Divide through by 4

10%2F4%3Cx%3C18%2F4

2.5%3Cx%3C4.5

The only two integers x between 2.5 and 4.5 are 3 and 4

So there are two sets:

x = 1st integer = 3
x+1 = 2nd integer = 4
x+2 = 3rd integer = 5
x+3 = 4th integer = 6
sum = 3+4+5+6=18

and

x = 1st integer = 4
x+1 = 2nd integer = 5
x+2 = 3rd integer = 6
x+3 = 4th integer = 7
sum = 4+5+6+7=22

Edwin