Question

jimmy read 2/15 of a book on monday,1/3 of it on tuesday, 2/9 of it on wednesday and 3/4 of the remainder on thursday. if he still had 14 pages left to read on friday, how many pages were there in the book?

Answer 1

Answer:

let the book have x pages

jimmy read

2/15 of a book on monday=(2/15)x

1/3 of the book on tuesday=(1/3)x

2/9 of it on wednesday =(2/9)x

so total page =

$(\frac{2}{15} + \frac{1}{3} + \frac{2}{9} )x \\ = ( \frac{6 + 15 + 10}{45} )x \\ = \frac{31}{45} x$

remaining pages are

(1-31/45)x={(45-31)/45}x=(14/45)x

on Thursdays he read 3/4 of remainder means 3/4 of (14/45)x

=(3/4)(14/45)x=(7/30)x

now

he still had 14 pages left to read

means

$x - ( \frac{31}{45} x + \frac{7}{30} x) = 14 \\ = > x - ( \frac{31}{45} + \frac{7}{30} )x = 14 \\ = > x - ( \frac{62 + 21}{90} )x = 14 \\ = > x - \frac{83}{90} x = 14 \\ = > x(1 - \frac{83}{90} ) = 14 \\ = > x( \frac{90 - 83}{90} ) = 14 \\ = > \frac{7}{90} x = 14 \\ = > x = 14 \times \frac{90}{7} \\ = > x = 2 \times 90 = 180$

book have 180 pages