A student opens a mathematics book to two facing pages. The product of the pages numbers is 420. Find the page numbers.
The first page is ? and the second page is ?
Thank you
n(n+1)=420
solve for n
The square root of 420 = 20.49
Let's try 20 and 21 as the facing pages. Is the product 420?
To find the page numbers, let's assign variables to the unknown numbers.
Let's say the first page number is "x" and the second page number is "x + 1" (since they are facing pages and the second page number is always one more than the first page number).
According to the given information, the product of the page numbers is 420. So we can set up the equation:
x * (x + 1) = 420
Expanding the equation:
x^2 + x = 420
Rearranging the equation:
x^2 + x - 420 = 0
Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.
Factoring:
(x + 21)(x - 20) = 0
Setting each factor equal to zero:
x + 21 = 0 or x - 20 = 0
Solving for x:
x = -21 or x = 20
Since the page number cannot be negative, we can ignore the x = -21 solution. Therefore, the first page number is 20.
Substituting x = 20 into x + 1, we find the second page number:
20 + 1 = 21
So, the first page is number 20 and the second page is number 21.
To find the page numbers, we need to solve for two unknowns. Let's denote the first page number as 'x' and the second page number as 'x + 1' (since they are facing pages).
Now, we are given that the product of these two page numbers is 420. So we can set up the equation:
x * (x + 1) = 420
To solve this equation, we can multiply out the terms:
x^2 + x = 420
Rearranging the equation, we can set it equal to zero:
x^2 + x - 420 = 0
Now, we have a quadratic equation. We can solve it by factoring or by using the quadratic formula. In this case, let's use factoring.
The quadratic equation can be factored as follows:
(x + 21)(x - 20) = 0
Setting each factor equal to zero and solving for x:
x + 21 = 0 or x - 20 = 0
x = -21 or x = 20
Since page numbers cannot be negative, we discard the solution x = -21. Therefore, the first page number is x = 20. And the second page number is x + 1 = 20 + 1 = 21.
So, the first page is 20 and the second page is 21.
You're welcome! If you have any additional questions, feel free to ask.