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 By: geniuskids (offline)  Sunday, May 06 2012 @ 10:20 PM CDT (Read 1261 times)
geniuskids

Pls help with solutions!

(Q10) Mr Lim had some stickers and stamps for his class. The number of stickers was half as many as the number of stamps. After each pupil received 3 stickers and 8 stamps from Mr Lim. he had 39 stickers and 2 stamps left. What was the total number of stickers and stamps Mr Lim had at first?

Thank you

Active Member

Registered: 11/12/11
Posts: 169

 By: geniuskids (offline)  Sunday, May 06 2012 @ 10:53 PM CDT
geniuskids

Also pls help with Questions 16 -Pattern

Don't understand the answer given as well. ..

Active Member

Registered: 11/12/11
Posts: 169

 By: echeewh (offline)  Monday, May 07 2012 @ 11:03 PM CDT
echeewh

hey there,

Following pls find worked solution for your Q10.

Method 1 ( Simultaneous Eqn method )
----------------------------------------------------

<Before>
S : P
1 : 2

<Process>
3 S and 8 P were given out to each pupil; hence the proportion given out is 3 : 8

<After>
39 : 2

Using Simultaneous Eqn method, we have ...

1p - 3u --> 39 --- (1)
2p - 8u --> 2 --- (2)

As question is asking for total number of both at first, we shall eliminate (u).

(1) x 8: 8p - 24u --> 312 --- (3)
(2) x 3: 6p - 24u --> 6 --- (4)

Subtracting (4) from (3) will eliminate (u).

8p - 6p --> 312 - 6
2p --> 306
1p --> 153

Therefore, total number of stickers and stamps = 3p --> 3 x 153 = 459

Method 2 ( Cross-Multiply method )
-----------------------------------------------

Using the above <Before> <After> models shown above, we have <Before> - <After> = <Process> / <Given Away> since the <After> model is using whole numbers ( actual qty ). Rewriting this, we have ...

S : P
1 : 2

-39 -2

3 : 8

Applying Cross-Multiply technique,

( 1u - 39 ) / 3 = ( 2u - 2 ) / 8
8 x ( 1u - 39 ) = 3 x ( 2u - 2 )
8u - 312 = 6u - 6
8u - 6u --> 312 - 6
2u --> 306
1u --> 153

Hence, total number of stickers and stamps = 3u --> 3 x 153 = 459

*NB. If these 2 methods / techniques dont work for you , then one can also use the standard Before and After model concept ( Drawing ) to derive the solution.

======================================

Trust the above helps.

Anything pls do clarify.

Regret to say this, I can do one question at a time and there are numbers of questions to attend to . Will do Q16 soon .

Cheers,
Edward

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Registered: 04/21/11
Posts: 627

 By: echeewh (offline)  Tuesday, May 08 2012 @ 09:31 PM CDT
echeewh

Q16 ( Pattern question )

Refer to Pattern shown on Paper.

Following is my worked solution:

Where n = Pattern Number,
Shaded Squares = (n + 1) x (n + 2) + 4
Unshaded Squares = (n x 2) + (n + 2) = 3n + 2

(a) Shaded Squares in Pattern 55
= (56 x 57) + 4 = 3196

(b) Number of Squares in Pattern 250
= ((251 x 252) + 4) + ((3 x 250) + 2)
= 63256 + 752
= 64008

* Solution provided for (b) requires one to merge the above 2 equations together ( in which case I doubt a primary student can do ).
Merging the 2 gives (n + 2) x (n + 4), that is why the solution provided as ( 252 x 254 )

====================================================

Trust this helps.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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