Question

Bethany wrote the equation x+(x+2)+(x+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?

A) Bethany is correct because consecutive odd integers will each have a difference of two.
B) 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.
C) Bethany is incorrect because 2 and 4 are even numbers, she should use 1 and 3 in their place.
D) Bethany is incorrect because consecutive integers always increase by 1 each time, not by 2.

Answer 1

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

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

After the information stated we can conclude that:

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.

Answer 2

Bethany is correct because consecutive odd integers will each have a difference of two.

For example: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...] All those are odd numbers, and have a difference of two.

So every time time we make 'x' an odd number in Bethany's equation, we will get three consecutive numbers.

For example, if 'x' equals '1', then we will get the three consecutive numbers 1, 3 and 5.

If 'x' equals 7, then we will get the three consecutive numbers 7, 9 and 11.