product of two consecutive numbers?

Question

Sean opens a book and notes the page numbers of the facing pages. The product of the two numbers is 1190. What are the page numbers of the facing pages ?

How should I explain/solve it to a P5 student ?

Answer 1

The page numbers are "very near" to each other, so the square root of 1190 will be "very near" to the average of the two page numbers.

sqrt(1190) = 34.496...

Now it should be obvious by looking at it.

Answer 2

If the pages are numbered n and n+1, then:

n x (n+1) = 1190
=> n^2 + n - 1190 = 0.
=>(n-34)(n+35) = 0.

since n can't be negative, that means n = 34. therefore the pages are numbered 34 and 35.

Answer 3

k(k+1) = 1190

k^2 + k = 1190

k^2 + k - 1190 = 0

k = (-1+/- (sq root)(1+4*1190))/2
= (-1 + 69)/2 or ( -1 -69)/2
= 68/2 or -70/2
= 34 or -35

Since k is the page number, it has to be positive. Therefore, k = 34, and k+1 = 35.

Check Answer :
34 * 35 = 1190

Therefore, the page numbers are 34 and 35.

Answer 4

Let the values of the page numbers be x and x + 1 respectively

x(x + 1) = 1190
x^2 + x = 1190
x^2 + x - 1190 = 0
x^2 - 34x + 35x -1190 = 0
x(x - 34) + 35(x - 34) = 0
(x - 34)(x + 35) = 0
x = 34, -35
x cannot be negative.
So the pages are 34 and 35

Answer 5

34 35

Answer 6

let x be the page number of the first page.

first page -- x
second page -- x+1

therefore: x (x+1) = 1190
x^2 + x = 1190
x^2 + x - 1190 = 0

x = 34

thus the page numbers are 34 and 35.

Answer 7

34 and 35

Answer 8

THE PAGE NUMBERS ARE 34&35.

Answer 9

34 & 35

Answer 10

34 & 35