Question

Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.

Answer 1

31

Explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

`x = (-b\pm√(b^2 -4ac) )/(2a)`

a = 1, b = 1 and c = -930

`x = (-1\pm√(1^2 -4(1)(-930)) )/(2(1))\\\\= (-1\pm√(1 +3720) )/(2)\\\\= (-1\pm√(3721) )/(2)\\\\= (-1\pm61 )/(2)\\`

`x = (-1-61 )/(2)\;\;\;\;or\;\;\;\;x= (-1+61 )/(2)\\\\\implies x = (-62 )/(2)\;\;\;\;or\;\;\;\;x= (60 )/(2)\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30`

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31