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]