The left hand page number was?

Question

Con opened his book and laid it down. He noticed that when the two page numbers showing in his book were multiplied together the answer was 1190. The right hand pages had odd numbers.

The left hand page number was

 

a. 30               b. 34                 c. 36              d. 40

Answer 1

let x and x+1 be the consecutive pages

x(x+1)=1190

x²+x=1190

x²+x-1190=0

1190=119*10=7*17*2*5

17*2=34 and 7*5=35

35-34=1

(x+35)(x-34)=0

x-34=0

x=34

x+1=35

b. 34 is the answer

Another simpler solution:You are multiplying two consecutive numbers together to get 1190.

Take the square root of 1190 and get 34.496.

The page numbers are 34 and 35.

 

Answer 2

The left and right hand pages should be exactly one number apart in a book. So let's call the right page number n, then the left page number (the odd number) would be n + 1.

 

(n)(n + 1) = 1190

n² + n = 1190

n² + n + 1/4 = 1190 + 1/4

(n + 1/2)² = 4761/2

n + 1/2 = √(4761/4)

n + 1/2 = 69/2

n = 69/2 - 1/2

n = 68/2 = 34

 

Note: you could also just use the quadratic formula at step 2; just subtract 1190 from both sides to get

n² + n - 1190 = 0

 

Also note that I ignored the negative square root of 4761/4 at step 5. Another answer is -35, but that answer doesn't apply to the book-page-number situation we care about.