Question

David had 2 bags of marbles. After he had sold 44 marbles from Bag X to his friend, the number of marbles in Bag Y was 5/7 of the number of marbles in Bag X. Given that there were 2/5 as many marbles in Bag Y as in Bag X originally, find the number of marbles in Bag X at first.

Answer 1

David had 2 bags of marbles. After he had sold 44 marbles from Bag X to his friend, the number of marbles in Bag Y was 5/7 of the number of marbles in Bag X. Given that there were 2/5 as many marbles in Bag Y as in Bag X originally, find the number of marbles in Bag X at first.
solution:
         let Number of marbles in bag X = x
               and number of marbles in Bag Y = y
According to question ,
                       y = 2/5 x .... (Given Original Condition)
                After David   sold 44 marbles from Bag X ,
                     number of marbles in Bag X = x - 44
                    y = 5/7 (x - 44) .............. (given)
         Substitute y = 2/5x in above equation , we get
                       2/5x = 5/7 (x -44)
                       2x/5 = 5x/7 - 5*44/7
                       5x/7 - 2x/5 = 5*44/7
                       by cross Multiplication ,
                   25x - 14x /(5*7) = 220/7
                   11x /35 = 220 /7
                 11x = 35*220/7
                   11x    = 5*220
                   x = 5*220 /11
                     x = 5*20
                   x = 100

Hence total Number of Marbles in Bag X is 100 .

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Answer 2

Let Number of marbles in bag X = x
               and number of marbles in Bag Y = y
According to question ,
                       y = 2/5 x .... (According to question)
                After David   sold 44 marbles from Bag X ,
                     number of marbles in Bag X = x - 44
                    y = 5/7 (x - 44) .............. (given)
         Substitute y = 2/5x in above equation , we get
                       2/5x = 5/7 (x -44)
                       2x/5 = 5x/7 - 5*44/7
                       5x/7 - 2x/5 = 5*44/7
                       by cross Multiplication ,
                   25x - 14x /(5*7) = 220/7
                   11x /35 = 220 /7
                 11x = 35*220/7
                   11x    = 5*220
                   x = 5*220 /11
                     x = 5*20
                   x = 100

Hence, total Number of Marbles in Bag X is 100 .

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