Posts Tagged ‘Word problem’

Here is a word problem:

Adam and Rahmad shared some beads. If Adam gave 1/3 of his share to Rahmad, Rahmad would have 70 more than Adam. If Adam gave 1/5 of his share to Rahmad, Rahmad would have 10 more than Adam. How many beads does Adam have at first?

The following is the bar model drawn with BarModelMaker. Please click on the model to see an animation showing how the model was draw.


From the model, we can see that we can divide Adam’s beads into 15 units. In the first scenario, Adam gives 5 units to Rahmad; and in the second scenario, Adam gives 3 units to Rahmad. So in the second scenario the difference between Rahmad and Adam is 4 units less than the difference between them in the first scenario. The 4 units causes the difference between Rahmad and Adam to be reduced from 70 to 10. And therefore 4 units represent 60 beads, and 1 unit represents 15 beads. So Adam has 15*15=225 beads.

Here is the BarModel script for this model:

add bar title=Adam1
add bar title=Rahmad1
add box size=a to bar[1]
add box size=r to bar[2]
cut box[1] into 3
shift box[1, 3] to bar[2]
update box[2,2] fill=green
box[1, 1 to 2] + 70 = box[2, 1 to 2]
add bar title=Adam2
add bar title=Rahmad2
add box size=a to bar[3]
add box size=r to bar[4]
cut box[3] into 5
shift box[3, 5] to bar[4]
update box[4,2] fill=cyan
box[3, 1 to 4] + 10 = box[4, 1 to 2]
cut box[1, 1 to 3] into 5
cut box [2, 2] into 5
cut box[3, 1 to 5] into 3
cut box[4, 2] into 3
add label title=70 position=above size=70 alignment=right to box[2,6]
add label title=10 position=above size=10 alignment=right to box[4,4]

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