SOLUTION: a man has a bag of sweets he gave 1 sweet to his son then he gave 1/7 of remaining sweets to his son. Then he gave 2 sweets to his daughter then he he gave 1/7 of remaining to his

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a man has a bag of sweets he gave 1 sweet to his son then he gave 1/7 of remaining sweets to his son. Then he gave 2 sweets to his daughter then he he gave 1/7 of remaining to his       Log On


   

Question 817688: a man has a bag of sweets he gave 1 sweet to his son then he gave 1/7 of remaining sweets to his son. Then he gave 2 sweets to his daughter then he he gave 1/7 of remaining to his daughter. Both child got equal numbers of sweets. What were the total sweets in the bag? Solve with explanation . .
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

a man has a bag of sweets he gave 1 sweet to his son then he gave 1/7 of remaining sweets to his son. Then he gave 2 sweets to his daughter then he he gave 1/7 of remaining to his daughter. Both child got equal numbers of sweets.

Let 'T' represent the total sweets in the bag.  

     Son: S+=+1+%2B+%281%2F7%29%28T-1%29

Daughter: D+=+2+%2B+%281%2F7%29%28T-2-S%29

Question states***Both child got equal numbers of sweets.

S+=+2+%2B+%281%2F7%29%28T-2-S%29

  7S = 14 + T - 2 - S

  8S - 12 = T

S+=+1+%2B+%281%2F7%29%28%288S-12%29-1%29   |Substitute for T

    7S = 7 + 8S - 13

      S = 6  (D=6)   and T = 36 total sweets in the bag  (8S -12)