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 By: layhongong (offline)  Monday, June 04 2012 @ 07:16 AM CDT (Read 1372 times)
layhongong

1)Mr Leong won some money in a lucky draw.
He spent 1/3 of the money and the additional \$20 on a wallet.
Next, he gave his family a treat which he spent \$30 and 3/5 of the remaining money.
Finally, he bought a shirt and had \$18 left.
If the shirt cost \$138 less than what he had spent on the treat, what was the amount of money Mr Leong won in the lucky draw?

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Registered: 04/09/11
Posts: 2

 By: GIM (offline)  Monday, June 04 2012 @ 09:17 AM CDT
GIM

Not sure if i am correct, this is my answer:
T=>Total
R=>remainder

Since 3/5R+30+18=(18+S)+138
And (18+S) is 2/5R

1/5R.....138-30-18=90
R………..90×5=450

2/3T……450+30+20=500
T…………500×3/2=750
He won \$750 in the lucky draw.

Regular Member

Registered: 11/07/10
Posts: 70

 By: GIM (offline)  Monday, June 04 2012 @ 09:18 AM CDT
GIM

Not sure if i am correct, this is my answer:
T=>Total
R=>remainder

Since 3/5R+30+18=(18+S)+138
And (18+S) is 2/5R

1/5R.....138-30-18=90
R………..90×5=450

2/3T……450+30+20=500
T…………500×3/2=750
He won \$750 in the lucky draw.

Regular Member

Registered: 11/07/10
Posts: 70

 By: mlteo (offline)  Monday, June 04 2012 @ 09:26 PM CDT
mlteo

Good work, GIM.

Do you have a solution using model construction ?

Would appreciate if you cangive us from that perspective.

Thanks.

Newbie

Registered: 12/31/06
Posts: 10

 By: GIM (offline)  Sunday, June 17 2012 @ 05:34 AM CDT
GIM

This should be the correct solution

T: Total
R: Remainder

Model----[_____1/3T_____][_____1/3T_____][____1/3T_____]
_______|<-------------------->|<-->| |
Wallet--------->(1/3T+\$20)|
Remainder--------------------------->[1/5R][1/5R][1/5R][1/5R][1/5R]
__________________________|<------------------->|<-->|
Treat---------------------------------->(3/5R+\$30 )
___________________________________________-|<------>|
Shirt & left--------------------------------------------------------->(S+\$18)

S---------->Treat - \$138
S----------> (3/5R + \$30) - \$138
S----------> 3/5R - \$108

2/5R -----> \$30 + S + \$18
substitute above S,
2/5R-----> \$30 + (3/5R - \$108) + \$18
2/5R-----> 3/5R - \$60
1/5R-----> \$60
R---------> \$60 x 5 = \$300

2/3T-----> \$20 + \$300 = \$320
T---------> \$320 x 3/2 = \$480 (answer)

Regular Member

Registered: 11/07/10
Posts: 70

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