beckee529 wrote:
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?
A. 10
B. 12
C. 15
D. 16
E. 18
m15 q20so i was able to set up the equation correctly
[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536
my question is without a calculator on the test what is the easiest way/ best plan of attack to realize that
x^2 + 16x - 1536 is...
(x + 48) (x - 32)
x = 32
then finally 480/x = 480/32 = 15 which is the answer
there was no way i was able to do this within 2 minutes.. too much factorizing and room for error.. for those larger quadratic equations. would backsolving be a good option here? please advise, thanks.
Algebra is one way of doing it. Another is by plugging in values. As usual, we start with the middle value so that we can go up or down depending on whether the days are short or in excess.
Say number of days = 15
The Tom reads 480/15 = 32 pages everyday.
In 5 days, he reads 32*5 pages which when split equally across the rest of the days such that each day gets 16 pages gives us 32*5/16 = 10 days
These 10 days are 5 less than 15 and hence everything fits.
Answer (C)
Of course, we could have needed to do this calculation once again in case (C) did not fit.
For example, trying (B), 480/12 = 40 pages
So in 5 days, the pages read = 40*5. When we try to split them equally among the leftover days such that each day gets 16 pages, we do not get an integral number of days. Hence this will not be the answer.
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Karishma
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