Q&A - PSLE Math

[MathIsFun]

[quote]Mary has some red pens and some blue pens in the pencil box. If she removes 1 red pen from the pencil box, then 3/8 of the remaining pens in the pencil box are red. If we put back the red pen and remove 3 blue pens instead, then 5/11 of the remaining pens in the pencil box are red. Find the number of red and blue pens.[/quote]
Let r be the number of red pens.
Let b be the number of blue pens.

5(r-1) = 3b
=> 5r-5 = 3b
=> 5r = 3b+5 (Eq1)
=> 30r = 18b+30 (Eq2)

6r = 5(b-3)
=> 6r = 5b-15
=> 30r = 25b-75 (Eq3)

Substitute Eq3 into Eq2,
25b-75 = 18b+30
=> 25b = 18b+105
=> 7b = 105
=> b = 15 (Eq4)

Substitute Eq4 into Eq1,
5r = 45+5
=> r = 10

Therefore, there are 10 red pens and 15 blue pens.

[corneyAmber]

http://i53.tinypic.com/6ozdyf.jpg\">

[MathIzzzFun]

PiggyLalala:

Need Help.

Mary has some red pens and some blue pens in the pencil box. If she removes 1 red pen from the pencil box, then 3/8 of the remaining pens in the pencil box are red. If we put back the red pen and remove 3 blue pens instead, then 5/11 of the remaining pens in the pencil box are red. Find the number of red and blue pens.
TIA

Hi

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cheers.

[adanial]

ksi:

tianzhu:

[quote=\"ksi\"]
Hi tianzhu,
Can you check if my solution above is correct based on the revised fraction by adanial? Thanks.

Hi ksi

The store sold 15 TV, 10 fans and 20 WM.

But it had only 3 fans in the store.

That’s why I think some numbers may not be in order in the question.

Best wishes

Yes you are right...the numbers are illogical. :salute:[/quote]Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

[corneyAmber]

adanial:

Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

Hi adaniel, do you know the answer for this question?

[tianzhu]

adanial:

Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

Hi adanial

Based on the original question, you can still arrive at a solution, however it defies logic.

Consider a group of 3 TV, 2 fans and 4 WM.

The cost per group is (3*1350) + (2*102) + (4*640) or 4050+204+2560.
This adds up to $6814 per group.

34070/6814 --- 5
Hence, you’ve 5 groups.
This means the shop sold 15 TV, 10 fans and 20 WM.

3 units ----- 45
4 units ----- 60

The shop had 60 items in the beginning.
3 parts or 36 are for TV, leaving a remainder of 24 for fans and WM.
1/8 of this remainder are for fans, this means 3 fans and the remaining 21 are for WM.

Here we’ve an awkward situation where the number of fans sold (10) is more than the number of fan in the store (3).

If you change 3/5 to 1/3 and 12.5% to 25%, the question will be more logical.

Best wishes

[Concerndad]

2/5 x 100% = 40% (% of TV)

100% -40% = 60% (%of remainder)
12.5% x 60% = 7.5% (% of fans)
60% - 7.5% = 52.5% (% of washing machines wm)

3 x 1350 = 4050 (3units of tv)
2 x 102 = 204 (2units of fans)
4 x 640 = 2560 (4units of wm)
4050 +204 + 2560 = 6814

34070/ 6814 = 5 (5sets)

3units+2units+4units =9units
9x5=45 (total no. of items sold off during sales)

3units - 45
1 units - 15
4units - 60 (total items in the stores)

52.5% of 60 = 31.5 ?? (Hmm…paiseh…is there something wrong in the question?)



Question 2

1st day - 20%
2nd day - 60
total for 1st and 2nd days - 20% + 60

2units -> 20% + 60 (if can draw model to show will be clearer)
1 unit -> 10% + 30
7units -> 70% + 210

therefore 30% -> 210
10% -> 210/3 = 70
100% -> 70 x 10 = 700

the jigsaw puzzle consist of 700pcs.

[adanial]

ksi:

adanial:

Hi Tianzhu, Ksi,
Ive checked the paper again... the numbers are correct. I'm puzzled how did the teacher solve this one.. lol
thank for the help.

Hi adaniel, do you know the answer for this question?

Hi Tianzhu, the answer is 21

[linden2000]

Alternative solution to Q2


1st day
Completed - 2units
Uncompleted - 8units
Total 10 units

2nd day
Completed - 2 units
Uncompleted - 5 units
Total 7 units

Since the total number of pieces is unchanged, equate total units on both days to a common number (lowest common multiple).

So
1st day
Completed 2x7=14
uncompleted 8x7=56
total 70

2nd day
Completed 2x10=20
uncompleted 5x10=50
total 70

Change in number completed =20-14=6
so 6 units = 60
1 unit = 10
Total number of pieces = 70 units = 70x10= 700

[blitz]

Can some kind soul please help with the following?


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Sorry, I omitted the Y when drawing. It is above T.

THe above figure shows a rectangle PQRS. PYR is a straight line and XYZ is parallel to SRT. Given that PX=10cm, TR=9cm and ZR =4cm, find the shaded area of rectangle XYTS.