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Jerry, Kumar and Lucas shared a bag of marbles. The number of

marbles Kumar had was 1/2 of the number of marbles Lucas had.

Jerry had 1/4 of the total number of marbles. Lucas had 36 more

marbles than Jerry.

 

(a)  What fraction of the marbles did Lucas have?

(b)  How many marbles were there altogether?

 Nov 5, 2021
 #1
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Let total number of marbles in the bag were = x

Given, then jerry has marbles = 1/4 of the total number of marbles

                                         
                                                 = 1/4= x/4

       
          Lucas had marbles = x/4 + 36 = (36 more than Jerry)

 

          Kumar had marbles = 1/2 of the number of marbles

                                                was had

 

                                           = 1/2 (x/4 + 36)

 

 

          As, there were total x marbles in the bag

           So;

                    x = x/4 + (x/4 + 36) + 1/2(x/4 + 36)

                     
                       = 2x/4 + x/8 + 36 + 18

                    x = \( {4x+x \over 8}\) + 36 + 18

 

                   x- 5x/8 + 54

                      3x/8 = 54

                           x = \( {54 * 8 \over 3} = {432 \over 3} = 144\)

 

x = 144

a) 

   Lucas had marbles = (x/4 + 36)

 

                                   = 144/4 + 36

 

                                     = 36 + 36

                                      = 72

      So;     Lucas had 1/2 of the total marbles.

 

    b)     Total marbles were x = 144.

 Nov 6, 2021

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