Question

student opened her math book and computed the sum of the numbers on two facing pages. Then she turned to the next page and computed the sum of the numbers on these two facing pages. Finally, she computed the product of the two sums, and her calculator displayed the number 69,165. What were the four page numbers?

Answer 1

130, 131, 132, 133

Explanation:

Let the first page numbe be x, the next x+1, x+2, x+3

The sum of the first two will be x+x+1=2x+1

The sum of the last two will be x+2+x+3=2x+5

Product will be (2x+1)(2x+5)

Since the product equals 69165

(2x+1)(2x+5)=69165

`4x^(2)+10x+2x+5=69165\\4x^(2)+12x+5=69165\\4x^(2)+12x-69160=0\\x^(2)+3x17290\\(x-130)((x+130)=0\\x=130, -133`

Therefore, x=130

Next pages are 131, 132, 133