SOLUTION: Mike was given some problem sums to complete. He completed 5/9 of the questions on Monday, 2 questions on Tuesday and 15 fewer questions than 4/11, of the remaining questions on We

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Mike was given some problem sums to complete. He completed 5/9 of the questions on Monday, 2 questions on Tuesday and 15 fewer questions than 4/11, of the remaining questions on We      Log On


   

Question 1199746: Mike was given some problem sums to complete. He completed 5/9 of the questions on Monday, 2 questions on Tuesday and 15 fewer questions than 4/11, of the remaining questions on Wednesday. Given that he had 57 questions left to complete on Thursday, find the number of questions Mike was given at first.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the original number of questions.
                solved               left to solve
    -------------------------------------------
     Monday     (5/9)x               (4/9)x
     Tuesday      2                  (4/9)x-2
     Wednesday  (4/11)((4/9)x-2)-15   57
     Thursday    57                    0

All the questions were finished by Thursday:

%28%285%2F9%29x%29%2B%282%29%2B%28%284%2F11%29%28%284%2F9%29x-2%29-15%29%2B%2857%29=x
%28%285%2F9%29x%29%2B%282%29%2B%28%2816%2F99%29x-8%2F11-15%29%2B%2857%29=x
%2855%2F99%29x%2B2%2B%2816%2F99%29x-8%2F11-15%2B57=%2899%2F99%29
44-8%2F11+=+%2828%2F99%29x
476%2F11=%2828%2F99%29x
x=%2899%2F28%29%28476%2F11%29=%28476%2F28%29%2899%2F11%29=17%2A9=153

ANSWER: 153

CHECK:
start: 153
Monday: finished (5/9)153 = 85; remaining 153-85 = 68
Tuesday: finished 2; remaining 68-2 = 66
Wednesday: finished (4/11)(66)-15 = 24-15 = 9; remaining 66-9 = 57