Let's determine the page numbers on the facing pages of a book, given that their sum is 89. Here's the detailed, step-by-step solution:
1. First, we need to understand that the pages of a book are numbered sequentially. If one page is on the left, its corresponding facing page on the right will be the next consecutive number.
2. Let's denote the left page number as [tex]\( x \)[/tex]. Since the right page is the next page, it would be [tex]\( x + 1 \)[/tex].
3. According to the problem statement, the sum of these two consecutive page numbers is 89. Therefore, we can write the following equation:
[tex]\[ x + (x + 1) = 89 \][/tex]
4. Simplify the equation by combining like terms:
[tex]\[ 2x + 1 = 89 \][/tex]
5. Next, we need to isolate [tex]\( x \)[/tex]. Subtract 1 from both sides of the equation to get rid of the constant term on the left:
[tex]\[ 2x + 1 - 1 = 89 - 1 \][/tex]
[tex]\[ 2x = 88 \][/tex]
6. Now, divide both sides of the equation by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{88}{2} \][/tex]
[tex]\[ x = 44 \][/tex]
7. Therefore, the number on the left page is [tex]\( 44 \)[/tex].
8. Since the right page is the next consecutive number, the number on the right page is:
[tex]\[ x + 1 = 44 + 1 = 45 \][/tex]
So, the facing pages with a sum of 89 are numbered 44 and 45.
