a student opens a mathimatic book to two facing pages. The product of the page numbers is 930. Find the page numbers.
Find the square root of 930.
What do you think these two page numbers are?
Pages are 30 and 31
30x31=930
To find the page numbers, we need to set up an equation based on the given information. Let's call the smaller page number "x" and the larger page number "x + 1" since they are two consecutive numbers.
We know that the product of the page numbers is 930, so we can write the equation as:
x * (x + 1) = 930
Now, let's solve this equation to find the page numbers:
Expanding the equation: x^2 + x = 930
Rearranging the terms: x^2 + x - 930 = 0
This is a quadratic equation, and we can solve it by factoring or using the quadratic formula. In this case, factoring is a bit tricky, so we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 1, and c = -930. Substituting these values into the quadratic formula:
x = (-1 ± √(1^2 - 4 * 1 * -930)) / (2 * 1)
x = (-1 ± √(1 + 3720)) / 2
x = (-1 ± √(3721)) / 2
x = (-1 ± 61) / 2
Using both the plus and minus options, we have two possible values for x:
x = (-1 + 61) / 2 = 60/2 = 30
x = (-1 - 61) / 2 = -62/2 = -31 (ignoring this negative value since page numbers cannot be negative)
Therefore, the smaller page number is 30 and the larger page number is 30 + 1 = 31.
The page numbers are 30 and 31.