Q&A - PSLE Math

[Vanilla Cake]

YLH88:

Percentage P6 2010 SA2 SHHK P2 Q16

Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4 : 1. As a result, Tricia had 2½ times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many stamps did Lena give to Tricia? [5 marks][Answer given: 150 stamps]

Hi YLH88,
To solve this 5-mark question, you need to apply repeated identity concept and then use unchanged total concept.

Yanling had 60% more stamps than Lena means:
Yanling : Lena
160% : 100%
Divide by 20
8 : 5

Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 5
5 : 20

You need to make Yanling to be equal in terms of ratio for both scenarios in order to compare the three of them. Note that ratio of Yanling is 8 in the first scenario and 20 in the second scenario.
LCM (Lowest or least common multiple) of 8 and 20 is 40.

So, you multiply by 5 and 2 in both scenarios and you will get :
Yanling : Lena
8 : 5
Multiply by 5
40 : 25

Tricia : Yanling
5 : 20
Multiply by 2
10 : 40

Before
Yanling: Lena : Tricia
40 : 25 : 10

Yanling and Lena gave Tricia some stamps in the ratio 4 : 1. As a result, Tricia had 2½ times as many stamps as before.
Tricia (in the end) = 2.5 times as many stamps as before -> 2.5x10=25

After
Yanling: Lena : Tricia
? : ? : 25

The increase for Tricia = 25u-10u = 15u
15 units is split in the ratio of 4 : 1 for Yanling and Lena.
Yanling-> 4/5x15u=12u
Lena-> 1/5x15u= 3u

Yanling (after): 40u-12u = 28u
Lena (after): 25u-3u= 22u

After
Yanling: Lena : Tricia
28 : 22 : 25

Yanling had 300 stamps more than Lena in the end ->
28u-22u= 300 stamps
6u = 300 stamps
u = 50 stamps

Number of stamps that Lena gave to Tricia -> 3u = 3x50 = 150 stamps.

VC's mum

[Dharma]

YLH88:

Hi all,


Need help urgently on the below question :

Percentage P6 2010 SA2 HHK P2 Q16
Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4 : 1. As a result, Tricia had 2½ times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many stamps did Lena give to Tricia? [5 marks][Answer given: 150 stamps]

I saw somewhere in the post the solution is :
[quote]Y L T
--------------------------------------------------
8 : 5 : 2 = 40 : 25 : 10
- 4 : - 1 : + 5 = - 12 : - 3 : + 15
--------------------------------------------------
28 22 25
--------------------------------------------------

\t6 u --> 300
\t1 u --> 300/6 = 50

\t3 u --> 3 x 50 = 150 stamps

\tIt was 50 stamps.

But I don't understand why need to change the ratio to 40 : 25 : 10 and
-12 : -3 : +15 :?

Need to know the answer urgently as PSLE maths paper is tomorrow :?:

Thank you![/quote]L : 10u – 1p -------------------------------------- ( 1 )
YL : 16u – 4p ------------------------------------- ( 2 )
T : 4u + 5p = 10u => [ 4u x 2.5 = 10u] -------- ( 3 )

6u = 5p ------------ From ( 3 )
16u – 4p = 10u – 1p + 300 ----------------- ( 2) = ( 1 ) + 300
6u = 3p + 300
5p = 3p + 300
2p = 300
1p = 150
No. of stamps Lena gave to Tricia = 1p = 150

[YLH88]

Hi VC's mum, Dharma,


Thank you so much for the solution!!

But I'm still abit confused :

Based on VC's mum's solution :
Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 5
5 : 20

Why do we divide by 5 ? I tried using divide by 25, which will give me 1 : 4 and can't get the answer.

Based on Dharma's solution :

L : 10u – 1p -------------------------------------- ( 1 )
YL : 16u – 4p ------------------------------------- ( 2 )
T : 4u + 5p = 10u => [ 4u x 2.5 = 10u] -------- ( 3 )

Why do you change the at 1st ratio to 10 : 16 : 4 ?

I tried using T : Y : L = 2 : 8 : 5 because I change Y : L to 8 :5 and T : Y to 1 : 4, so combining both set I get 2 : 8 : 5, and I can't get the answer

Sorry still blur ... :?

[Vanilla Cake]

YLH88:

Hi VC's mum, Dharma,

Thank you so much for the solution!!
But I'm still abit confused :

Hi YLH88,
You are always welcome!
My DD1 took PSLE 2008 and DD2 will be taking PSLE 2011, so I know how you feel about PSLE exam. BTW, is your DS taking HMT?

YLH88:

Based on VC's mum's solution :
Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 5
5 : 20

Why do we divide by 5 ? I tried using divide by 25, which will give me 1 : 4 and can't get the answer.

Yes, you can divide by 25 and you will still get the same answer:

Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 25
1 : 4

Yanling had 60% more stamps than Lena means:
Yanling : Lena
160% : 100%
Divide by 20
8 : 5

For Yanling, LCM of 4 and 8 is 8. So, multiply by 2 and you will get:
Tricia : Yanling
1 : 4
Multuply by 2
2 : 8

Before
Yanling: Lena : Tricia
8 : 5 : 2
Multiply by 5
40 : 25 : 10

The rest of the steps is the same.

VC's mum

[YLH88]

Vanilla Cake:

YLH88:

Hi VC's mum, Dharma,

Thank you so much for the solution!!
But I'm still abit confused :

Hi YLH88,
You are always welcome!
My DD1 took PSLE 2008 and DD2 will be taking PSLE 2011, so I know how you feel about PSLE exam. BTW, is your DS taking HMT?

YLH88:

Based on VC's mum's solution :
Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 5
5 : 20

Why do we divide by 5 ? I tried using divide by 25, which will give me 1 : 4 and can't get the answer.

Yes, you can divide by 25 and you will still get the same answer:

Tricia had 75% fewer stamps than Yanling means:
Tricia : Yanling
25% : 100%
Divide by 25
1 : 4

Yanling had 60% more stamps than Lena means:
Yanling : Lena
160% : 100%
Divide by 20
8 : 5

For Yanling, LCM of 4 and 8 is 8. So, multiply by 2 and you will get:
Tricia : Yanling
1 : 4
Multuply by 2
2 : 8

Before
Yanling: Lena : Tricia
8 : 5 : 2
Multiply by 5
40 : 25 : 10
The rest of the steps is the same.

VC's mum

Hi VC's mum,

Nope, my DS not taking HCL, so last day will be next Monday, I can relax after that ..... phew ...

So sorry, why do we need to multiple by 5 ?

[tianzhu]

Hi YLH88


This question touches on the concept of unchanged total quantity.

The stamps are transferred internally but the total number of stamps remains the same in the beginning as well as in the end.

You may solve it using MD or Units method. I suggest using the UM for this question.

A student should be familiar with the concept of equivalent ratios so as to handle this question well.

You’ll notice that Yan Ling is repeated in comparisons with Lena and Tricia. Therefore we have to make Yan Ling’s units the same when comparing.

Once you understand the concept, the rest is just selecting comfortable equivalent units where one can work out the calculations more easily. In this particular question, 15 units is a reasonable number. Why? It can easily be divided into the ratio of 4:1 and also it very neat to increase 10 units by 15 units to 25 units.

It just leaves me to wish your kid a very successful PSLE 2010.

Best wishes

http://farm5.static.flickr.com/4104/5056458756_e8f2996118_b.jpg\">

[YLH88]

Hi VC’s mum, Dharma, TianZhu,


Thank you for the solution! Finally I understand, we changed by multiply by 5 is to suit the question for easy computation. Sigh… must be the stress and very nervous that’s why my brain not working properly…

Thank you thank you!!

[BigDevil]

http://postimage.org/image/2ryb5fmmc/

I can work out the answer to be a)90 ; b)$16.80. But could someone tell me what is the best method to use to solve this question?

[tianzhu]

Hi


Hope this helps.

Best wishes.

http://farm5.static.flickr.com/4144/5059076235_e9518fc671_b.jpg\">

[iFruit]

BigDevil:

http://postimage.org/image/2ryb5fmmc/

I can work out the answer to be a)90 ; b)$16.80. But could someone tell me what is the best method to use to solve this question?

Easier to apparch this as backward problem..

Let the total number of coins at the end = 100u

so at the end,

50 cent coins = 40u,
20 cent coins = 30u,
10 cent coins = 30u

Then at the beginning,

10 cent coins = 5/2 (30u) = 75u
20 cent coins = 4/3(30u) = 40u
50 cent coins = 40u + 18

75u = 40u + 18 + 24---> 35u = 42---> u = 6/5

10 cent coins in beginning = 75(6/5) = 90

question (b) follows easily from thereon..