Q&A - PSLE Math

[2632parent]

Kindly help me on this question


1) There are some pupils in the school hall. If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls. If, instead of 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls. What fraction of the pupils in the school hall are girls?

Thank you

[Michaelia0816]

I did not know how, I examined the Question for about 2-4 hours but still sun know so I have not choice but to ask

[CDE]

tianzhu:

CDE:

Hi, can anyone g ive the explanation & working on the following:


A rectangle divides a plane into 2 region at the most. How many regions at the most can 5 such identical rectangles divide the plane into?

No picture or anything else given. The answer is 82 regions, but how :?
TIA.

Hi

Where is this question from?

I get an answer of 16(dividing the plane into regions).

Best wishes

Hi Tianzhu,
It's from MO advanced by Terry Chew chapter 11, qn 6.
Their solution is:

Number of rectangle 1. 2. 3. 4. 5
Number of regions. 2. 10. 26. 50. 82
Increase in no. Of regions. 0. 8. 16. 24. 32

Five rectangles can divide a plane into 82 region.

Despite of the explanation above,I still don't get it.

[Michaelia0816]

Oh, I understood, Kept on calculating wrongly, but my idea is similar to yours!

[Michaelia0816]

Thanks!

[Michaelia0816]

Pls help with my two last questions for today,


Web:
http://t.co/oDgX6LaJ
http://t.co/iac86CSu

[tianzhu]

Michaelia0816:

http://t.co/oDgX6LaJ

Hi girl

Good Morning.

Volume of water in Tank A ------- 40*30*60 -------- 72000

Height of water in Tank A and B (figure 2) -------- 72000 /(40*30) + (45*40) ------- 72000/(1200 + 1800)

Height of water in Tank A @figure 2 ------ 24 cm

Best wishes

[MathIzzzFun]

2632parent:

Kindly help me on this question


1) There are some pupils in the school hall. If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls. If, instead of 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls. What fraction of the pupils in the school hall are girls?

Thank you

Hi

There are some pupils in the school hall. If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls. If 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls. What fraction of the pupils in the school hall are girls?

If 1 girl leaves the school hall, Girls : Boys --> 1 : 6
If 1 girl & 2 boys leaves the school hall, Girls : Boys --> 1:4
number of girls remain the same (1 girl leaves),
2u --> 2, 1u --> 1
Girls in hall --> 1 + 1 =2
Boys in hall --> 6
Girls as fraction of pupils in hall = 2/8 = 1/4


There are some pupils in the school hall. If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls. If, instead of 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls. What fraction of the pupils in the school hall are girls?

If 1 girl leaves the school hall, Girls : Boys --> 1u : 6u
therefore, number of Girls : Boys --> 1u + 1 : 6u

If 2 boys leave hall, girls : boys --> 1:4
so, Girls : Boys
--> 1u + 1 : 6u - 2
= 1 : 4

cross multiply,
4u + 4 = 6u - 2
1u --> 3
Number of Girls --> 3+1 = 4
Number of Boys --> 6 x 3 = 18
Total --> 22
Fraction of pupils that are girls --> 4/22 = 2/11

cheers.

[tianzhu]

2632parent:

Kindly help me on this question


1) There are some pupils in the school hall. If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls. If, instead of 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls. What fraction of the pupils in the school hall are girls?

Thank you

Hi

Good Morning.

A neat way is to use MD. To save some time, I’ll just give some pointers.

Case 1 ----- If 1 girl leaves the school hall, then 1/7 of the remaining pupils are girls.

1 girl + 1 box (unit)(girls) + 6 boxes (units)(boys)

Case 2 ------ If, instead of 1 girl, 2 boys leave the school hall, then 1/5 of the remaining pupils are girls.

1 part (girls) + 4 parts (boys) +2 boys

1 part ----- 1 unit + 1

Compare the MD for case 1 and 2

4 units + 4 + 2 ------- 6 units

2 units ------- 6

1 unit ------ 3

Number of girls ------ 1 unit + 1 ------ 4

Number of boys ------ 6 units ------- 18

Fraction of the pupils in the school hall who are girls -------- 4/22 ------- 2/11

Best wishes

[tianzhu]

CDE:

tianzhu:

Despite of the explanation above,I still don't get it.

Hi

Good Morning.

Thank you for your response.

I am not familiar with the scope of Maths Olympiad requirement.

I would imagine a plane to be like a flat sheet.

It’s clear enough to visualise a rectangle cutting a plane into 2 regions.

I’d imagine having a plane in the form of a thin rectangular piece of cake lying on a table. A knife representing the rectangle is used to make a line on top of the cake to divide into 2 regions.

Next, cut another line, this time, we’ll have 4 regions.

For the 3rd cut, we’ll get 7 regions

For the 4th cut, 11 regions

For the 5th cut, 16 regions.

Best wishes