Q&A - PSLE Math

[tianzhu]

Hi Belle2011


Good Morning.

In this question, we use a strategy called “Working Backwards”.

We need to recognize that the two fractions are of different measures --- fraction of a tin of cookies and fraction of a single piece of cookie.

Before I begin, I want to emphasise that you may also do this question without MD if you are able to visualise the flow of events without the help of a picture.

I’ve included MD in my solution as it’ll help students to see the transactions.

I’ll try to break down the solution into four steps to show the flow of events, hope it’s useful to you.

After B took 5/6 of the remaining tin of cookies, 1/6 of the tin was left. This 1/6 of tin comprises of 1/3 of a cookie and the remaining 2 cookies, therefore 1 unit equals 2 1/3.

Once you become more familiar with this strategy, you may consolidate into one MD as shown in my earlier solution.

Best wishes

http://farm6.static.flickr.com/5211/5487752786_819943e736_b.jpg\">

[Belle2011]

tianzhu:

Hi Belle2011


Good Morning.

In this question, we use a strategy called “Working Backwards”.

We need to recognize that the fractions are of different measures --- fraction of a tin of cookies and fraction of a single piece of cookie.

Before I begin, I want to emphasise that you may also do this question without MD if are able to visualise the flow of events without the help of a picture.

I’ve included MD in my solution as it’ll help students to see the transactions.

I’ll try to break down the solution into four steps to show the flow of events, hope it’s useful to you.

After B took 5/6 of the remaining tin of cookies, 1/6 of the tin was left. This 1/6 of tin comprises of 1/3 of a cookie and the remaining 2 cookies, therefore 1 unit equals 2 1/3.

Once you become more familiar with this strategy, you may consolidate into one MD as shown in my earlier solution.

Best wishes

http://farm6.static.flickr.com/5211/5487752786_819943e736_b.jpg\">

Dear tian-zhu,
Thank very much for sharing another way of presenting the solution.
I was stuck with \"After B took 5/6 of the remaining tin of cookies...\".
So 5/6 * 1/6 = 5/36.
I am thinking \"my gosh! 5/36, how to draw the model...\".
Anyway, I am trying to reduce the number of 5 mark problem sums which I can't solve to as low as possible and you have been helping me all along.
Once again, thanks a lot.
Cheers,
Belle.

[tisha]

Need help with this question:


Susan takes 2 hrs to travel from Town A to Town B. Helen takes 3 hrs to travel from Town B to Town A. How long will it take for both Susan and Helen to meet along the way?

[ozora]

small:

is_me_lblue:

Hi,


I am stuck again.

Amos'salary is 20% more than Steve's but 20% less than Joe's. If their total salary is $2220,find Amos's salary.

I always get the answer of 740 but answer given is 720.

Thank you

Hi,

HTH..


The key step is to calculate Joe's percentage. Given that Amos's salary is 20% less than Joe's.

80% of Joe = 120% of Amos
100% of Joe = 150% of Amos

Steve = 100% (10 Units)
Amos = 120% (12 Units)
Joe = 150% (15 Units)

37 Units = 2220
1 Unit = 60
12 Unit = 720

or
370% = 2220
1% = 6
120% = 720.

to anyone,
can someone enlighten how 100% of Joe = 150% of Amos?
I can't catch any clues on how to derive it.

[Apphia]

Fazillah, Linda and Winnie each owned a collection of comics. The total collection owned by Linda and Winnie was 3/2 as many comics as Fazillah owned. Linda owned 4/5 as many comics as the total collection owned by Fazillah and Winnie. If Winnie owned 169 fewer comics than Linda, how many comics must Fazillah and Linda each give to Winner in order for the three girls to have the same number of comics?


Thank You.

[ADoc]

LaiHeng:

small:

[quote=\"is_me_lblue\"]Hi,


I am stuck again.

Amos'salary is 20% more than Steve's but 20% less than Joe's. If their total salary is $2220,find Amos's salary.

I always get the answer of 740 but answer given is 720.

Thank you

Hi,

HTH..


The key step is to calculate Joe's percentage. Given that Amos's salary is 20% less than Joe's.

80% of Joe = 120% of Amos
100% of Joe = 150% of Amos

Steve = 100% (10 Units)
Amos = 120% (12 Units)
Joe = 150% (15 Units)

37 Units = 2220
1 Unit = 60
12 Unit = 720

or
370% = 2220
1% = 6
120% = 720.

to anyone,
can someone enlighten how 100% of Joe = 150% of Amos?
I can't catch any clues on how to derive it.[/quote]Hi, I believe there was a typo error in the answer above.
It should be 100% of Joe = 150% of Steve instead of Amos.

Hope this clarifies.
cheers
ADoc

[ADoc]

tisha:

Need help with this question:


Susan takes 2 hrs to travel from Town A to Town B. Helen takes 3 hrs to travel from Town B to Town A. How long will it take for both Susan and Helen to meet along the way?

Hii! Hope this is useful.
Key Concept: to understand net speed, i.e. 2 objects or persons moving at different speeds along the same distance but from opposite direction is equivalent to one single object/person covering the same distance but at a rate or a net (sum) speed of the original 2 objects/persons

The same concept is applicable to questions concerning filling / draining water tanks.


|--------- 1U ---------|
[------------><--------]

------------->
Susan's speed = Distance / Time = 1U / 2hr = (1/2)U per hr

<--------
Helen's speed = 1U / 3hr = (1/3)U per hr

net speed or total speed = (1/2) + (1/3) = (5/6) U per hr
this means that for every hr, the total distance covered by Susan & Helen = (5/6)U

Hence, the time required to cover the entire distance AB = distance / total speed = 1U / (5/6)U = 1 x (6/5) = (6/5) hr = 1 & (1/5) hr

Ans: It will take 1 & (1/5) hr for Susan & Helen to meet along the way.

Check: In (6/5) hr, Susan will cover (6/5) divide by 2 = (3/5)U
Helen will cover (6/5) divide by 3 = (2/5)U
Total distance = 1U

[tisha]

Thank you ADoc for the solution.

[ADoc]

Apphia:

Fazillah, Linda and Winnie each owned a collection of comics. The total collection owned by Linda and Winnie was 3/2 as many comics as Fazillah owned. Linda owned 4/5 as many comics as the total collection owned by Fazillah and Winnie. If Winnie owned 169 fewer comics than Linda, how many comics must Fazillah and Linda each give to Winner in order for the three girls to have the same number of comics?


Thank You.

Hi! Glad to help! My advice is to use the ratio method for efficiency. Model would give the same ans certainly but too cumbersome for this question in my opinion. Sorry if the solution looks lengthy. I just wanna be as clear as I can for each step of workings.

cheers!
ADoc

key concept: total collection of comics remains unchanged, hence convert the total ratio units to be equal

(L+W) : F = 3 : 2 (total = \"5\")
(F+W) : L = 5 : 4 (total = \"9\")

Since total collection of comics must be the same, therefore observing the above ratio units, student must be able to determine the common multiple or denominator = 5 x 9 = 45

(L+W) : F = 3 : 2 = (3 x 9) : (2 x 9) = 27 : 18 (total 45 units)
(F+W) : L = 5 : 4 = (5 x 5) : (4 x 5) = 25 : 20 (total 45 units)

Now we have:
F = 18U
L = 20U
L+W = 27U, therefore W = 27 - 20 = 7U or simply 45 - 18 - 20

How many comics = 1U?
since W has 169 fewer comics than L:
L - W = 20 - 7 = 13U = 169
1U = 169 / 13 = 13 comics

For each girl to have the same number of comics, it means each must have 45 / 3 = 15U

we can evaluate this in different ways, here's one:
F: 18U - 15U = 3U
3U = 3 x 13 = 39 comics

L: 20U - 15U = 5U
5U = 5 x 13 = 65 comics

ans: Fazillah & Winnie must give Linda 39 & 65 comics respectively in order for the three girls to have the same number of comics.

[ADoc]

tisha:

Thank you ADoc for the solution.

Hi Tisha! You're most welcome!
cheers!