In the question "Find two consecutive even integers whose sum is 126" If the answer was 61.5 what would the next consecutive number be?

Answer 1

Consecutive can apply to a list of numbers that can be counted with integers -- there is a 1st and 2nd and 3rd etc items.

Real numbers such as 61.5 are too many and cannot be put in such a list.

So if you got this answer, then you did something wrong. Lets see how to think about this.

We need 2 consecutive even numbers. So if n is the first number then n is even, right? The number consecutive to n is n+1 but that would be odd (think here that the positive integers go 1,2,3,4,5,... ie odd, even, odd, even, odd....) so the next consecutive EVEN number is not n+1 but the one after that ie n+2

So our two consecutive EVEN numbers are n and n+2.

Their sum must be 126 so we can write that as n + (n+2)=126.

Open the brackets to get n+n+2=126

......... combine like terms to get 2n+2=126

......... subtract 2 from both sides to get 2n=124

......... divide by 2 to get n=62

......... which makes the other number n+2=64

indeed 62 and 64 are consecutive even numbers (the number in between them is 63 which is odd and doesn't count) and indeed 62+64=126.

Answer 2

See the solution that I entered. Bear in mind that the question asks for integers and 61.5 is not an integer.