The sum of four odd integers is 296. What is the greatest of the four consecutive odd integers

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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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.

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step-by-step explanation: