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Math

Jessica is an avid reader. She bought a copy of the best seller book 'Math is Beautiful'. On the first day, Jessica read 1/5 of the pages plus 12 more, and on the second day she read 1/4 of the remaining pages plus 15 pages. On the third day, she read 1/3 of the remaining pages plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book ?

A.120
B.180
C.240
D.300
E.360

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  1. There are 9 tried and true problem solving methods.
    If an algebraic solution perplexes you... perhaps a guess and check is a better "first" attempt.
    The question gives you choices for the answer...
    What if you start at the top with the a) 120 pages
    Then times it by 1/5 and add 12, then take that away from your 120
    So after the first day if you started with 120 pages you would have 120 - 36
    that is 84 pages on the start of day 2
    take 84 multiply by 1/4 and add 15 for the total pages read that day
    84 - 36 = 48
    So right away you know that 120 pages is TOO FEW because you are already down to 48 pages left to read, but the problem says you have 62 pages after the first day...
    Do you kinda see the "guess and check" method?
    Now you try b) 180 and see if you get 62 pages left after the last day of reading.

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  2. X = Total pages.

    1st Day: x - x/5 -12 = 4x/5 - 12 remaining.

    2nd Day: (4x/5-12) - (4x/5-12)/4 - 15 = 4x/5-12 - x/5-3 - 15 = 3x/5 - 30 remaining.

    3rd Day: (3x/5-30) - (3x/5-30)/3 - 18 = 3x/5-30 - x/5 - 10 - 18 = 2x/5 - 58
    remaining.

    2x/5 - 58 = 62,
    X = 300 Pages.

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