Percentage P6 2010 SA2 River Valley P2 Q18

Susan has some vanilla and chocolate sweets in her bag. If she adds 20 vanilla sweets into the bag, the percentage of vanilla sweets in the bag becomes 40%. If she adds 30 chocolate sweets, there will be 70% of chocolate sweets in the bag. How many vanilla and chocolate sweets does she have? [5 marks][Answer given: 64 vanilla sweets and 126 chocolate sweets]  X wrong answers provided

   
Model Drawing
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40 : 60 = 2 : 3

    [   ][   ][   ][10][   ][   ][   ][10]             
V [                                 ] [    20  ]
C [                      ][                     ][                      ]
    [   ][   ][   ][10][   ][   ][   ][10][   ][   ][   ][10]<30>  Compare

30 : 70 = 3 : 7

V [   ][   ][   ][   ][   ]
C [   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ]  Compare


5 u --> 3 x 10 + 30 = 60
1 u --> 60/5 = 12

6 u --> 6 x 12 = 72 vanilla sweets
14 u --> 14 x 12 = 168

168 - 30 = 138 chocolate sweets

She has 72 vanilla and 138 chocolate sweets.


Alternative method (Partial model)
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   [                   ][ 20 ]  4 u - 20
V [     ][     ][     ][     ]
C [     ][     ][     ][     ][     ][     ]

V [     ][     ][     ]                                        x 7 --> 21  p
C [     ][     ][     ][     ][     ][     ][     ]         x 3 --> 21 p
   [                                          ][ 30 ]  6 u + 30

7 x (4 u - 20) --> 3 x (6 u + 30)
28 u - 18 u --> 90 + 140
10 u --> 230
1 u --> 230/10 = 23

4 u --> 4 x 23 = 92

92 - 20 = 72 vanilla sweets

6 u --> 6 x 23 = 138 chocolate sweets

She has 72 vanilla and 138 chocolate sweets.


Alternative method
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V                   C       
+ 20
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  2        :        3
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3 V + 3 x 20 --> 2 C
2 C --> 3 V + 60
6 C --> 9 V + 3 x 60 = 9 V + 180


V                 C
                 + 30
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3        :        7
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7 V --> 3 C + 3 x 30 = 3 C + 90
3 C --> 7 V - 90
6 C --> 14 V - 2 x 90 = 14 V - 180

14 V - 180 --> 9 V + 180
5 V --> 180 + 180 = 360
V --> 360/5 = 72 vanilla sweets

2 C --> 3 x 72 + 60 = 276
C --> 276/2 = 138 chocolate sweets

She has 72 vanilla and 138 chocolate sweets.