Q&A - PSLE Math

[Mum1113]

Hi, these 2 qns been posted here before but I just could’nt find the solutions. Could someone kindly help me out please ? Many many thanks !


Qn: David’s father picks him up from school every evening at 6pm. One day, David was dismissed early at 5pm. He walked home taking the same route that his father usually drives. When he met his father along the way he boarded the car and returned home 50 minutes earlier than usual. Given that his father drove at a constant speed and planned to reach school st 6pm sharp, how long in minutes, had he walked before he was picked up by his father ?


Qn: There are some red and blue pencils in a box. If 30 red pencils are taken out from the box, the total number of pencils left will be 8 times the number of red pencils left. If 50 blue pencils are taken out from the box, the total number of pencils left will be thrice that of blue pencils left. How many pencils are there in the box ?

[lizawa]

You can use ratio to solve this question.


Step 1 : list down all you know
A : B+C+D
= 2:5

B: A+C+D
= 1:2

A+B+D
= 1:3

Step 2: Make the parts equal
There are 7 parts for 1st ratio, 3parts for 2nd ratio and 4 parts for 3rd ratio
So the LCM for 7,3,4 is 84.

A : B+C+D
= 2:5
= 24:60

B: A+C+D
= 1:2
= 28:56

A+B+D
= 1:3
=21 : 63

Step 3 : More clue from question : D paid $30 less than C
Look at 3rd ratio, C = 21u, hence D = 21u - 30
From 3rd ratio :
A+B+D = 63u
A+B = 63u - D = 63u - (21u-30) = 42u +30

From 1st and 2nd ratio,
A = 24u, B = 28u
Equate :
24u + 28u = 42u +30 (solve for u)
10u =30
1u = 3

Cost of present = 84u = 84 * $3 = $252

Hint : to check, just find out how much A,B, C and D pays and substitute back to the original ratio. You will get the same ratio => answer is correct.

[tianzhu]

Hi


Hope this helps.

Best wishes.

http://farm3.static.flickr.com/2039/5736224632_00ab5b5c9a_z.jpg\">

[Mum1113]

Thanks tianzhu....as usual the illustration is impressive !


Will u get to the other one as well ?
Qn: There are some red and blue pencils in a box. If 30 red pencils are taken out from the box, the total number of pencils left will be 8 times the number of red pencils left. If 50 blue pencils are taken out from the box, the total number of pencils left will be thrice that of blue pencils left. How many pencils are there in the box ?

[tianzhu]

Mum1113:

Thanks tianzhu....as usual the illustration is impressive !

Will u get to the other one as well ?

Hi

You're welcome.

Here's the answer to your second question.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5147/5736014129_4b0176859f_z.jpg\">

[Mum1113]

thanks tianzhu, the colorful picture makes digestion easier (I don't mean dinner but the problem sum), cheers

[tianzhu]

Mum1113:

thanks tianzhu, the colorful picture makes digestion easier (I don't mean dinner but the problem sum), cheers

Hi Mum1113

Good Morning.

You're welcome.

Best wishes

[chrisu]

There are 800 children in Group A. 30% of the children in Group A were boys. There were 400 children in Group B. 60% of the children in Group B were boys. After some transfer between the two groups, 25% of the children in Group A and 75% of the children in Group B were boys. What is the transfer from Group B to A?


Note : My answer is 70 Girls were transfer from B to A. 30 Boys were transfer from A to B, though not needed. I got the answer using algebra and simultaneous equation which my daughter do not understand well.

Anyone can do with models or other easier to understand method. Thank you.

[Neat]

tianzhu:

Hi


A quick one for Q1

One needs to differentiate the ratios representing the number of legs and the number of animals. The ratios for the number of legs and the number of animals are of different measures.

The total number of ducks' legs to the total number of cows' legs is 5:9 ------ 20:36 (equivalent ratios)

A duck ----- 2 legs, a cow ----- 4 legs

This means the total number of ducks to the total number of cows ----- 10:9 -----20:18

Ducks ----- 20
Cows ----- 18

There are 38 ducks and cows.

Best wishes

[quote]tianzhu

What made you decide to multiply by 4 to get the equivalent ratio?

Pls enlighten.
[/quote]

[tianzhu]

Neat:

What made you decide to multiply by 4 to get the equivalent ratio?

Hi

We are given that the total number of ducks and cows is between 20 and 40.

We are also given the ratio of the total number of ducks' legs to the total number of cows' legs is 5:9.

Given this ratio, a student is expected to find out the number of animals.

A cow has 4 legs and a duck has 2 legs.

Hence, the number showing the number of cow’s legs has to be a multiple of 4.Likewise the number showing the number of duck’s legs has to be a multiple of 2.

That’s why we multiply the given ratios 5:9 by 4 to get 20:36.

This gives us 10:9 as the ratio for the number of ducks to the number of cows. This is not within the range of 20 and 40.

Multiply by 2 to get an equivalent ratio of 20:18 which is 38 and within the range.

Best wishes