## Bethany wrote the equation X+ (x+2)+(+4)= 91 when she was told that the sum of three consecutive odd integers had a sum of 91. Which s

Question

Bethany wrote the equation X+ (x+2)+(+4)= 91 when she was told that the sum of three consecutive odd integers had a
sum of 91. Which statement about her equation is true?

Bethany is correct because consecutive odd integers will each have a difference of two.
Bethany is correct because there are three xs in the equation and three is an odd number so it represents the sum of odd
numbers.
Bethany is incorrect because 2 and 4 are even numbers, she should use 1 and 3 in their place.
Bethany is incorrect because consecutive integers always increase by 1 each time, not by 2.

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2 weeks 2021-09-12T05:24:16+00:00 2 Answers 0

a

Step-by-step explanation:

Option A) Bethany is correct because consecutive odd integers will each have a difference of two

Step-by-step explanation:

The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4

So, the 3 odd integers will be:

x  , (x+2) and (x+4)

Their sum is given to be 91. So we can write:

x + (x+2) + (x+4) = 91

Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.

Other options are not correct because consecutive odd integers always increase by 2. For example, the next odd integer after 1 is 3, which is obtained by adding two, similarly the next odd will be 5 and so on.