Q&A - PSLE Math

[ChiefKiasu]

James Ang:

an interesting thinking question to share here.


Mainah had some money at first.she spent it all in 3 stores.In each store, she spent $2 more than half of what she had when she entered.
(a) How much did she spend at the last store?
(b)how much did she have at first?

(a) Amount spent in last store = S = S/2 + 2
=> Half of S = $2
=> S = $4

(b) Money Mainah had when entering 2nd store = $4 + $4 + $2 = $10
Money Mainah had when entering 1st store = $10 + $10 + $2 = $22

So Mainah had $22 at first.

[James Ang]

ChiefKiasu:

James Ang:

an interesting thinking question to share here.


Mainah had some money at first.she spent it all in 3 stores.In each store, she spent $2 more than half of what she had when she entered.
(a) How much did she spend at the last store?
(b)how much did she have at first?

(a) Amount spent in last store = S = S/2 + 2
=> Half of S = $2
=> S = $4

(b) Money Mainah had when entering 2nd store = $4 + $4 + $2 = $10
Money Mainah had when entering 1st store = $10 + $10 + $2 = $22

So Mainah had $22 at first.

hi Chief, it is a work backwards type of approach like what you did. But let's work forward to check with your final answer of $22 at first.

first store = 22/2 +2 = 11+ 2 = $13
left $9
second store = 9/2 +2= 4.50+2 = $6.50
left $2.50

I think the answer is $28, check
first store = 28/2 +2 = 14+ 2 = $16
left $12
second store = 12/2 +2= 6+2 = $8
left $4
third store = 4/2 +2 = $4
left $0

[Dharma]

ChiefKiasu:

James Ang:

an interesting thinking question to share here.


Mainah had some money at first.she spent it all in 3 stores.In each store, she spent $2 more than half of what she had when she entered.
(a) How much did she spend at the last store?
(b)how much did she have at first?

(a) Amount spent in last store = S = S/2 + 2
=> Half of S = $2
=> S = $4

(b) Money Mainah had when entering 2nd store = $4 + $4 + $2 = $10
Money Mainah had when entering 1st store = $10 + $10 + $2 = $22

So Mainah had $22 at first.

http://www.postimage.org/image.php?v=PqrmctA

[tianzhu]

Hi moderator


Please help to delete this post.

[trytry]

Emelyn:

Hi,


I have a question :

In a soccer stadium, the number of female to male spectators is 3:7. After 287 female and 287 male left the stadium, the ratio of female to male spectators became 2:5. How many spectators were there at first ?

Can someone help me solve ?

...........................F.................M................diff

Before.................3...................7.................4
After....................2...................5.................3


Since same number of female and male spectactors left the stadium, the difference between female and male spectactors remained the same before and after.

...........................F.................M................diff

Before.................3x3...................7x3.................4x3
............................=9..................=21.................=12

After....................2x4...................5x4.................3x4
............................=8....................=20................=12

therefore 9u-8u=1u---------------287
No of spectactors=(9+21)x287=8610

[Vanilla Cake]

tianzhu:

Hi

Hope this helps.

http://farm5.static.flickr.com/4032/4576248465_2371709985_o.jpg\">

http://farm5.static.flickr.com/4055/4576882662_68b0310776_o.jpg\">

Best wishes

Hi Tianzhu,
Thank you for your well-illustrated and crystal clear explanation.
For your reference and other readers, this is a 4-mark P5 Maths question from http://www.orlesson.org/orp/09Ma/2009-Math-SA1-CHS.pdf set on 14 May 2009.

Other than different methods posted by yourself and Dharma, trytry's ratio method is a fast and accurate way to solve this type of problem.This will save precious time for the child during critical Maths exams and allow him/her to have more time to tackle other questions in the Maths paper.

Before
F : M
3 : 7
9 : 21

After
F : M
2 : 5
8 : 20

Common difference for F = 1 ( 9-8 ) and M = 1 ( 21-20 )-This step is not necessary to include in the workings for this question.
u = 287
30u = 8610

There were 8610 spectators at first.

Mods - pls kindly merge this question in http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=173824#173824 for her to provide her model method of solving such problem sum as Tianzhu mentioned that it is quite challenging to draw models as the quantities at the beginning and at the end are different.

Thanks.

Submitted by VC's mum

[tianzhu]

Hi

Hope this helps.
http://farm4.static.flickr.com/3325/4576464109_8c4e672e2b_o.jpg\">

http://farm4.static.flickr.com/3301/4576464177_62832bdc8f_o.jpg\">

http://farm4.static.flickr.com/3337/4576464211_ccddbd0344_o.jpg\">

Best wishes

[tianzhu]

Hi


The use of Units and Parts is useful for solving problems involving two changed quantities. It is applicable to two different values as well as two numbers of the same values. Depending on the numbers given in the question, MD may not be appropriate in certain circumstances. But MD can be used to solve this genre of questions.

However, if the two changed numbers are the same value, it may be more efficient to use the Ratio Method as shown by VC.

I learn something new today.
Thank you, VC or rather VC’s mum.

Best wishes

[ChiefKiasu]

James Ang:

hi Chief, it is a work backwards type of approach like what you did. But let's work forward to check with your final answer of $22 at first.


first store = 22/2 +2 = 11+ 2 = $13
left $9
second store = 9/2 +2= 4.50+2 = $6.50
left $2.50

I think the answer is $28, check
first store = 28/2 +2 = 14+ 2 = $16
left $12
second store = 12/2 +2= 6+2 = $8
left $4
third store = 4/2 +2 = $4
left $0

Yes... paiseh... the second step should have been:
(b) Money Mainah had when entering 2nd store = $4 + $2 + $4 + $2 = $12
Money Mainah had when entering 1st store = $12 + $2 + $12 + $2 = $28

I'm not sure how one can solve this problem without working backwards.

Dharma's solution is pretty self-explanatory. Great job!

[tianzhu]

Hi


Another alternative is to use the Units Method.

http://farm4.static.flickr.com/3397/4577204580_0edd93c263_o.jpg\">

Best wishes