Opening a book with 2 facing pages. The product of the page numbers is 600. What are the page numbers?
x(x-1) = 600
x^2 -x -600 = 0
(x - 25 )(x + 24 )= 0
so 24 and 25
To find the page numbers, let's assign variables. Let the smaller page number be represented by "x" and the larger page number be represented by "y".
From the given information, we know that the product of the page numbers is 600. Therefore, we have the equation:
x * y = 600
Now, let's find the factors of 600:
Factors of 600: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
We can see that 24 and 25 are a pair of factors that give a product of 600.
So, the smaller page number (x) is 24, and the larger page number (y) is 25.
Therefore, the page numbers are 24 and 25.
To find the page numbers, we need to solve the equation related to the problem. Let's assume the first page number is 'x'. Since the second page is facing, the second page number will be 'x+1'.
According to the problem, the product of the page numbers is 600. So, we can set up the equation as follows:
x * (x + 1) = 600
To solve this equation, we can follow these steps:
1. Expand the equation:
x^2 + x = 600
2. Rearrange the equation:
x^2 + x - 600 = 0
Now we have a quadratic equation that we can solve for 'x'. We can do this by factoring, completing the square, or using the quadratic formula. For simplicity, let's factor the equation:
(x + 25)(x - 24) = 0
Setting each factor equal to zero, we have two possible values for 'x':
x + 25 = 0 --> x = -25
x - 24 = 0 --> x = 24
Since page numbers cannot be negative, we discard the -25 as a valid solution. Therefore, the first page number is 24, and the second page number (facing) is 24 + 1 = 25.
Hence, the page numbers are 24 and 25.