im having a hard time with this question and i just started high school a little while ago and I'm STRUGGLING so i was wondering if you guys could help a little bit

Question

Find three consecutive odd integers such that the sum of the first two is 25 less than the third.

Answer 1

Let's call the three consecutive odd integers x, x + 2, and x + 4, where x is the first integer.

According to the problem, the sum of the first two integers is 25 less than the third:

x + (x + 2) = (x + 4) - 25

Now, let's solve for x:

2x + 2 = x + 4 - 25

First, simplify the right side of the equation:

2x + 2 = x - 21

Now, subtract x from both sides:

x + 2 = -21

Subtract 2 from both sides:

x = -23

So, the three consecutive odd integers are:

x = -23

x + 2 = -21

x + 4 = -19

So, the three consecutive odd integers are -23, -21, and -19.

Answer 2

The three consecutive odd integers will be separated by even ones and therefore can be described as every other integer. They can be defined as x, x + 2 and x+ 4. Interestingly enough, the list would be the same if the question asked about consecutive even integers (it's the rest of the problem specs that will determine which).

The sum of the 1st two is x + (x + 2). 25 less than the 3rd is (x + 4) - 25. The equation is, therefore, x + x + 2 = x + 4 - 25. Combining like terms gives 2x + 2 = x - 21

Moving the x terms to the left side and the 2 to the right side gives x = -23. The other two odd numbers would then be - 21 and - 19. You can check to see that they satisfy the requirements as specified.