SOLUTION: 1.) Find three consecutive odd integers such that the sum of the first and third is 37 more than the second. 2.) The sum of 4 consecutive integers is at least 114. Find th

Question 4828: 1.)
Find three consecutive odd integers such that the sum of the first and third is 37 more than the second.

2.)
The sum of 4 consecutive integers is at least 114. Find the smallest possible values for the four numbers.
Answer by Abbey(339) (Show Source): You can put this solution on YOUR website!
we know that consecutive odd integers have a difference of 2:
Let x=first odd integer
Let x+2 = second odd integer
Let x+4 = third odd integer
the sum of the first and third is 37 more than the second:
x+(x+4)= 37 + (x+2)
2x+4=39+x
subtract x from both sides:
x+4=39
subtract 4 from both sides:
x=35
35 = first odd integer
37 = second odd integer
39 = third odd integer
This makes sense because 35+39=37+37
The sum of 4 consecutive integers is at least 114. Find the smallest possible values for the four numbers:
Let x= first consecutive integer
Let x+1 = second consecutive integer
Let x+2 = third consecutive integer
Let x+3 = fourth consecutive integer
x+(x+1)+(x+2)+(x+3)=114
4x+6=114
subtract 6 from both sides
4x=108
x=27
27 = first consecutive integer
28 = second consecutive integer
29 = third consecutive integer
30 = fourth consecutive integer
This makes sense because 27+28+29+30=114, and anything less would be less than 114.

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