Modelling sans Algebra

Singapore PSLE Modelling Math (for 11 year-old pupils)

Problem:

1) 20% of John saving is $120 more than 30% of Brian savings.

2) After John spent 5/6 of his saving and Brian spent 1/2 of his saving ,
John has $20 more than Brian.

Find the saving of John at first ?

Solution:
(Technique: work backwards from the End.)
Before 2nd condition:
J: 60 units+ $120
[1][2]…..[9][10] [$20]
[1][2]…..[9][10] [$20]
[1][2]…..[9][10] [$20]
[1][2]…..[9][10] [$20]
[1][2]…..[9][10] [$20]
[1][2]…..[9][10] [$20]
B: 20 units
[1][2]…..[9][10]
[1][2]…..[9][10]
After 2nd condition:
J: [1][2]…..[9][10] [$20]
B: [1][2]…..[9][10]
20% of J
= 0.2 x 60 units + 0.2 x $120
= 12 units + $24
30% of B
= 0.3 x 20 units
= 6 units
From 1st condition:
(12 units+$24)- 6 units
->$120
6 units +$24 ->$120
6 units ->$96
1 unit ->$16
J: 60 units+ $120
J= 60x$16+ $120= $1080
[QED]
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