Tom

[crackgmat007]

Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?

10
12
15
16
18

Can someone solve the quadratic pls?

[mp2437]

let x = # of pages per day Tom reads. Let t be the # of days it takes Tom to finish the book.

We know that x*t = 480. We also know that if Tom reads 16 pages more per day, it would take him 5 days less to complete the book (same number of pages). We write this as follows:

(x+16)*(t-5) = 480

So we have 480 = (x+16)*(t-5) = x*t
factor out: xt - 5x + 16t - 80 = xt
reduce like terms: -5x + 16t - 80 = 0, or 5x = 16t - 80, so x = (16t - 80) / 5

Plug this back into the original equation: xy = 480
(16t - 80)* t/5 = 480, or 16t^2 - 80t = 5 * 480

16t^2 - 80t - 2400 = 0, or when you reduce like terms,
t^2 - 5t - 150 = 0

Solve for t:
Quadratic Equation: (-(-5) + sqrt(5^2 - 4(1)(-150)))/2 = (5 + sqrt(625))/2 = 30/2 = 15 = t.

Negate the other root of the quadratic equation since time cannot be negative. Choice C is your answer.

[crackgmat007]

Thanks. This is a much easier equation than I got. This helps.