Fraction P5

2. Joshua had 2/3 as many game cards as Nat. After Joshua bought another 20 game cards and Nat lost 29 game cards, Joshua now has 4/5 as many game cards as Nat. How many game cards did Nat have at first?

  J         N      5J        4N

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   2   :   3      10   :    12

+20     -29   +100     -116

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   4   :   5      20   :    20

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10 u + 100 --> 12 u – 116

2 u --> 100 + 116 = 216

1 u --> 216 ÷ 2 = 108

3 u --> 3 x 108 = 324 game cards

Nat had 324 game cards at first.

Alternative method

J          [    4 u    ][20]                 2 : 3 = 4 : 6. Instead of

N         [            6 u           ]        using 2 and 4 units, use

                                  [29]         4 and 6 units (because of 4 p)

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           [1 u][5]    x   4

J          [       4 p       ]               Make use of J (before) to 

N         [         5 p          ]          construct J (after)

           [1 u][5]      x      5

6 u – 29 --> 5 u + 25               Compare N.

1 u --> 25 + 29 = 54

6 u --> 6 x 54 = 324 game cards

Nat had 324 game cards at first.