Q&A - PSLE Math

[excelhub]

Lazy snake:

Hi jieheng,need help in this question:

There were 590 fruits altogether.1/5 of the apples and 1/20 of the oranges make up 73 fruits.How many apples and oranges were there?

5/5 of the apples and 5/20 of the oranges = 73*5 = 365
hence 15/20 of the oranges = 590-365

and you will be able to work out the rest ?

[tianzhu]

mathnoobs:

Hi all, need help on the concept of inverse proportion rates and direct proportion rates.


As I understand it, water rates problems are direct proportion rates. As the number of taps increases, the amount of water flow increases, or the amount of job done increases.

People working on a job is inverse proportion rates. Ie.
5 cleaners takes 4 hours to clean a house. How long does 10 cleaners take to clean the same house ?
The answer would be 2 hours. As the number of cleaners increase, the time it takes to clean the house decreases, so the number of resources is inversely proportional to the time it takes to get the job done.

Taking the same reasoning, the water rate problem should also be an inverse proportion rate , as the number of taps increases, the amount of time it takes to get the job done (to fill the tank)decreases.

So, if I have a problem that says: 5 taps take 4 hours to fill a tank. How long does 10 taps takes to fill the same tank ? (assume all taps have the same rate) Would this be the same logic as the Cleaner problem ?

Hi

You are talking about two scenarios.

1) Direct proportion

Take this as an example, assume all taps have the same flow rates

Water flows from 1 tap ----- 500 cm3 per minute

In 20 minutes, water flowing into a tank from 1 tap------ 500*20 ------ 10000 cm3

In 20 minutes, water flowing into a tank from 5 taps ------ 5*500*20 ------ 50000 cm3

2) Inverse proportion, the answer to your question is 2 hours.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8111/8563349161_6f4bfb92a2_z.jpg\">

[tianzhu]

Lazy snake:

Hi jieheng,need help in this question:

There were 490 adults in an auditorium.When 3/7 of men and 5/9 of the women left the auditorium ,the total number of adults who remained became 240.How many men were at the auditorium at first?

Hi

This question touches on simultaneous concept.

You may solve it pictorially using MD or represent the variables with letters of the Alphabet or Units and Parts.

Men
Left the auditorium ------- 3M
Remained in the auditorium ------- 4M

Women
Left the auditorium ------- 5W
Remained in the auditorium ------- 4W

The total number of adults who remained became 240.

4M + 4W ------ 240
Hence, 1M + 1W ----- 60

3M + 5W ------ 250 (490-240)

3M + 3W + 2W ----- 250

180 + 2W ------ 250

2W ------ 70

1W ------ 35

This gives 1M ------ 25 (1M + 1W ----- 60)

Number of men@first ------- 7*25 ------ 175

Hope this helps.

Best wishes

[mathnoobs]

tianzhu:

mathnoobs:

Hi all, need help on the concept of inverse proportion rates and direct proportion rates.


As I understand it, water rates problems are direct proportion rates. As the number of taps increases, the amount of water flow increases, or the amount of job done increases.

People working on a job is inverse proportion rates. Ie.
5 cleaners takes 4 hours to clean a house. How long does 10 cleaners take to clean the same house ?
The answer would be 2 hours. As the number of cleaners increase, the time it takes to clean the house decreases, so the number of resources is inversely proportional to the time it takes to get the job done.

Taking the same reasoning, the water rate problem should also be an inverse proportion rate , as the number of taps increases, the amount of time it takes to get the job done (to fill the tank)decreases.

So, if I have a problem that says: 5 taps take 4 hours to fill a tank. How long does 10 taps takes to fill the same tank ? (assume all taps have the same rate) Would this be the same logic as the Cleaner problem ?

Hi

You are talking about two scenarios.

1) Direct proportion

Take this as an example, assume all taps have the same flow rates

Water flows from 1 tap ----- 500 cm3 per minute

In 20 minutes, water flowing into a tank from 1 tap------ 500*20 ------ 10000 cm3

In 20 minutes, water flowing into a tank from 5 taps ------ 5*500*20 ------ 50000 cm3

2) Inverse proportion, the answer to your question is 2 hours.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8111/8563349161_6f4bfb92a2_z.jpg\">

thanks Tianzhu. I see. The inverse proportion depends on the parameters involved. Some of the parameters relationship are direct proportion, some are inverse.

[marstolive]

Can someone help out with the explanations?


Two teams had to complete a certain job in 30days. 6 days after they started the job, one team was transferred to another zone while the other continued working alone and completed the remaining part of the job in 40 days.
In how many days could each team,working separately, complete the whole job.

I'm clueless
:thankyou:

[marstolive]

A painting can be completed by Picasso and Gogh working together for four days followed by Picasso working alone for another five days. If Gogh can complete 1/30 of the painting more than Picasso per day, how many days will they take to complete the painting if they work alone?


:imdrowning:
:thankyou:

[altp10]

Hi. Can someone help me with the following question?


Three children, Adam, Ben and Cyrus, shared a box of beads in the ratio of 5:3:4 and there were 4 beads left over. They shared these 4 beads together with a second box, containing 1/8 fewer beads than the first box, in the same ratio as before, and there was no reminder.
a) Find the total number of beads they shared in the first round.
b) Find the total number of beads Adam received in the end.

Thank you in advance.
Regards Anthony…

[tianzhu]

altp10:

Hi. Can someone help me with the following question?


Three children, Adam, Ben and Cyrus, shared a box of beads in the ratio of 5:3:4 and there were 4 beads left over. They shared these 4 beads together with a second box, containing 1/8 fewer beads than the first box, in the same ratio as before, and there was no reminder.
a) Find the total number of beads they shared in the first round.
b) Find the total number of beads Adam received in the end.

Thank you in advance.
Regards Anthony..

Hi

Quite an interesting question, where is it from?

It helps to draw MD.

1 part ----- 8

At first

60 + 4

In the end

56 + 4

Number of beads in the first round ------ 64

Beads received by Adam in the first round ------ 5/12*60 ------- 25

Beads received by Adam in the second round ------ 5/12*60 ------- 25

Total number of beads received by Adam ------- 50

Best wishes

[altp10]

Hi Tianzhu,


It’s from St. Andrews… 1st time I encountered this.

How did u derive the 1 part---- 8?
And the 60?

I understand that since the sharing ratio is 5:3:4 it means it would be a multiple of 12. But is a little bit of guess and check involved to attain the 60?

Thank u.

[tianzhu]

altp10:

Hi Tianzhu,


It's from St. Andrews.. 1st time I encountered this.

How did u derive the 1 part---- 8?
And the 60?

I understand that since the sharing ratio is 5:3:4 it means it would be a multiple of 12. But is a little bit of guess and check involved to attain the 60?

Thank u.

Hi

Yes, you may use GC, but it tends to be less efficient especially at upper primary level.

A neat way to solve this question is to use MD.

Hope this helps.

Best wishes

http://farm9.staticflickr.com/8515/8575849299_dec8bcbc97_z.jpg\">