A student opens a mathematics book to two facing pages. The product of the page number is 420. Find the page numbers.
The first page is ____
The second page is ____
Blaze it
Here's a hint: the square root of 420 is 20.49
Ms. Sue...I understand how to get the sqrt of 420, but after that I get lost. So what you typed is not making sense in my head ..ughhh
What do you get when you multiply 20 * 21?
420, so more or less I would have had to have found 2 numbers that equaled 420 when multiplied (which product means multiply 2 numbers)correct?
So my first page would be 20
Second page would be 21
Right.
Thank you very much for your help. I appreciate it very much!
You're very welcome.
To find the page numbers, we know that the product of the page numbers is 420. Let's denote the first page number as "x" and the second page number as "x+1" (since they are consecutive pages).
We can set up the equation:
x * (x+1) = 420
To solve this equation, we can start by expanding the equation:
x^2 + x = 420
Now, we rearrange the equation to bring everything to one side:
x^2 + x - 420 = 0
To further solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is a convenient way to find the page numbers.
Factoring the equation, we need to find two numbers whose product is -420 (since the middle term, "+x", has a positive coefficient) and whose sum is the coefficient of the middle term (which is 1).
After some trial and error, we find that the numbers are -20 and 21:
(-20) * 21 = -420
Now, we know that x = -20 or x = 21.
Since page numbers cannot be negative, we discard x = -20 and take x = 21 as the first page number.
Therefore, the first page is 21 and the second page is 21 + 1 = 22.