Answer: 77
Step-by-step explanation:
Let the four odd numbers be represented as a, b, c and d.
a + b + c + d = 296
b = a+2 ( since they are consecutive and odd)
c = a+4
d = a+6
Then, substitute the values gotten into the original equation. This will be:
a + (a+2) + (a+4) + (a+6) = 296
4a +2 +4 +6 = 296
4a +12 = 296
Then, collect like terms
4a + 12 = 296
4a = 296 - 12
4a = 284
Divide both sides by 4
4a/4 = 284/4
a = 71
If a is 71,
b = a + 2 = 71+ 2 = 73
c = a + 4 = 71 + 4 = 75
d = a + 6 = 71 + 6 = 77
The greatest of the four consecutive odd integers is 77.
We will find that the largest of the 4 consecutive odd integers is equal to 77.
We can write four consecutive odd integers as:
x, x + 2, x + 4, x + 6
Where x is an odd number.
Then, we have that the sum of these 4 numbers is equal to 296, so we have:
x + (x + 2) + (x + 4) + (x + 6) = 296
4*x + 12 = 296
4*x = 296 - 12 = 284
x = 284/4 = 71
This is the smallest of the 4 odd integers, the largest one will be:
71 + 6 = 77.
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