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 By: ricebowl1912 (offline)  Saturday, August 28 2010 @ 01:02 AM CDT (Read 14572 times)
ricebowl1912

Need help on the following 2 problem sum questions (pls provide workings) :

1) A cupboard has 3 shelves. There are 48 books altogether on the shelves. Mei Lin removed 8 books from the top shelf and placed them on the middle shelf. She removed 6 books from the middle shelf and placed them on the lowest shelf. As a result, 3 shelves had the same number of books. How many books were on the middle shelf at first?

2) Tom and Peter shared a sum of money. If Tom gave \$350 to Peter, they would have the same amount of money. If Peter gave \$100 to Tom, he would have half as much money as Tom. How much money did Tom had at first?

Newbie

Registered: 07/28/10
Posts: 5

 By: tanhuimin (offline)  Sunday, August 29 2010 @ 05:24 AM CDT
tanhuimin

1) A cupboard has 3 shelves. There are 48 books altogether on the shelves. Mei Lin removed 8 books from the top shelf and placed them on the middle shelf. She removed 6 books from the middle shelf and placed them on the lowest shelf. As a result, 3 shelves had the same number of books. How many books were on the middle shelf at first?

Solution :
Top Shelf -8
Middle Shelf +8 -6
Lowest Shelf +6

48/3 = 16
middle shelf +8 -6 = 16
middle shelf = 16 -2 = 14
Answer : 14 books were on the middle shelf at first.

2) Tom and Peter shared a sum of money. If Tom gave \$350 to Peter, they would have the same amount of money. If Peter gave \$100 to Tom, he would have half as much money as Tom. How much money did Tom had at first?

Tom gave \$350 to Peter, and they would have the same amount of money implies that Tom has \$700 mode than Peter
use this as a base to draw a model.

From the model, (see attached)
1u = 100 + 700 + 100 = 900
Tom has 2 x 900 - 100 = 1700.
Answer : Tm has \$1700 at first.

Junior

Registered: 12/31/06
Posts: 18

 By: ricebowl1912 (offline)  Friday, September 03 2010 @ 08:06 AM CDT
ricebowl1912

Newbie

Registered: 07/28/10
Posts: 5

 By: rathanackumr (offline)  Sunday, September 05 2010 @ 08:51 PM CDT
rathanackumr

Model method attached. Cheers!

Junior

Registered: 07/22/10
Posts: 18

 By: rathanackumr (offline)  Sunday, September 05 2010 @ 10:33 PM CDT
rathanackumr

Model method for 2nd question attached. cheers!

Junior

Registered: 07/22/10
Posts: 18

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