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.
