Q&A - PSLE Math

[2DMommy]

Please help me with these 2 questions :

1)At first , Shop X has 156 kg of rice flour and Shop Y has 72 kg of rice flour. After each shop sold the same quantity of rice flour, the amount of rice flour that Shop X has was 4 times that of Shop Y. How many kilograms of rice flour did Shop X sell ?

2)An equal number of male and female runners took part in the National Education Marathon last year. 960 male runners and 350 female runners quit running and did not complete the marathon. The number of male runners left was 1/6 the number of female runners. What was the total number of runners at the start of the marathon ?

Thank you.

[mrswongtuition]

2DMommy:

Please help me with these 2 questions :

1)At first , Shop X has 156 kg of rice flour and Shop Y has 72 kg of rice flour. After each shop sold the same quantity of rice flour, the amount of rice flour that Shop X has was 4 times that of Shop Y. How many kilograms of rice flour did Shop X sell ?

2)An equal number of male and female runners took part in the National Education Marathon last year. 960 male runners and 350 female runners quit running and did not complete the marathon. The number of male runners left was 1/6 the number of female runners. What was the total number of runners at the start of the marathon ?

Thank you.

Question 1:
Constant Difference (the difference between the amounts of flour at each shop did not change).

156 - 72 = 84
Shop X has 84kg of flour more than Shop Y.

Since the amount of flour shop X has is 4 times as much as Shop Y after they each sold an equal quantity of flour:
X [--][--][--][--]
Y [--]<-84kg-->

3 units --> 84kg
1 unit --> 84/3 = 28kg
Shop Y had 28kg of flour left.

Since Shop X and Shop Y sold the same amount of flour, we can find out how much flour shop Y sold to get the answer:
72 - 28 = 44kg
Shop X sold 44kg of flour.



Question 2:

Start off drawing 'equal number at first':

M [----------------------------------------]
F [----------------------------------------]

Then add in 960 males left (and males are left with 1 unit),
350 females left (and females are left with 6 units):
M [u][-----------960-------------------]
F [u][u][u][u][u][u][-------350------]

From the above model, we can see that 5 units is 960 minus 350:
5 units --> 960-350 = 410
1 unit --> 82
There were 82 males left.

82 + 960 = 1042
There were 1042 males at first.

Since there were equal numbers of males and females, we can simply multiply the number of males by 2 to get the answer:
1042 x 2 = 2084
There were 2084 participants at first.

[2DMommy]

Thank you mrswongtuition for the clear explanation.


Needed help again for these two questions.

1)2/5 of Raju’s money is equal to 1½ of Carls’ money. When Raju spent $450 and Carl received $120, the ratio of Raju’s money to Carl’s money became 5 : 2. How much money did Raju have at first ?\t\t\t\t\t\t\t\t\t
2) Mr Smith had 1.5 l of white paint in Tin A and 1.25 l of red paint in Tin B. He poured 750 ml of red paint from Tin B into Tin A. Then he poured some of the mixture in Tin A back into Tin B.\t If 7/11 of the final mixture in Tin B was made up of red paint, what was the volume of the mixture in Tin A that Mr Smith had poured into Tin B ?\t

Thank you !

[MathIzzzFun]

2DMommy:

Thank you mrswongtuition for the clear explanation.


Needed help again for these two questions.

1)2/5 of Raju's money is equal to 1½ of Carls' money. When Raju spent $450 and Carl received $120, the ratio of Raju's money to Carl's money became 5 : 2. How much money did Raju have at first ?\t\t\t\t\t\t\t\t\t
2) Mr Smith had 1.5 l of white paint in Tin A and 1.25 l of red paint in Tin B. He poured 750 ml of red paint from Tin B into Tin A. Then he poured some of the mixture in Tin A back into Tin B.\t If 7/11 of the final mixture in Tin B was made up of red paint, what was the volume of the mixture in Tin A that Mr Smith had poured into Tin B ?\t

Thank you !

Hi
1)
2/5 of Raju’s money = 3/2 of Carl’s money
--> 6/15 of Raju’s money = 6/4 of Carl’s money

So, at first:
Raju’s money --> 15u
Carl’s money --> 4u

After Raju spent $450 and Carl received $120,
15u - $450 : 4u + $ 120
= 5 : 2

Cross-multiply --> 30u - $ 900 = 20u + $600
10u = $ 1500 --> 1u = $ 150
15u = $ 2250

Raju had $ 2250 at first.

2)
After 750ml was poured from Tin B into Tin A,
amount of white paint : red paint, in Tin A --> 1.5l : 0.75l = 2 : 1

After mixture of Tin A as poured into Tin B,
total amount of red paint in Tin B --> 7u
amount of white paint in Tin B --> 4u

Since the white paint came from Tin A, and white paint : red paint from Tin A is in ratio of 2 : 1,
amount of red paint from Tin A mixture --> 2u

So, amount of red paint from Tin B --> 7u-2u = 5u
5u --> 1.25l - 750 ml = 500 ml , 1u --> 100ml
Volume from Tin A mixture --> 4u + 2u = 6u = 600 ml


cheers.

[elkniwt]

jesschan:

And does anyone have the complete question to Q18 of paper 2? The total area of triangles A & B is missing in my copy.


Many thanks!

Dear jesschan,

It is also blank on my copy. But I think it is 125% (my guess), cos I could get the answer 3/22 using this value.

Here's the question. I put in 125% in red (only my guess).
http://i44.tinypic.com/1zr1jq9.jpg\">

Dear tianzhu and MathIzzzFun,
I only know how to do this question using simultaneous equations. :oops: Could you please help to advise how to do this question in suitable method. Thank you very much.

[sleepyqueen]

jesschan,

Here is it based on elkniwt's upload:
http://i41.tinypic.com/1z676s4.jpg\">

[pixiedust]

Thanks all for help with Q18, my copy also has the missing '125%'.


My brain is rusty after the holiday ! I would appreciate any help with the following questions - if no time for a full solution, just the units statements will do.Thanks !

Source : NYPS 2011 P6 CA1 Paper 2
http://i1197.photobucket.com/albums/aa424/pixie_dust8/ksp2012/q11.jpg\">
-> I am confused bythe 3/4 of a bead and \"no bead is to be divided in any way\", this should be remainder concept and to use branch method ?

http://i1197.photobucket.com/albums/aa424/pixie_dust8/ksp2012/q14.jpg\">
-> I have problems forming the Day 2, 10% increase for Females !

http://i1197.photobucket.com/albums/aa424/pixie_dust8/ksp2012/q17.jpg\">
-> this is external transfer but the number transferred out is expressed in ratios, how to for the units statements?


SOS! SOS! SOS !
THANKS IN ADVANCE !

[MathIzzzFun]

elkniwt:

jesschan:

And does anyone have the complete question to Q18 of paper 2? The total area of triangles A & B is missing in my copy.


Many thanks!

Dear jesschan,

It is also blank on my copy. But I think it is 125% (my guess), cos I could get the answer 3/22 using this value.

Here's the question. I put in 125% in red (only my guess).
http://i44.tinypic.com/1zr1jq9.jpg\">

Dear tianzhu and MathIzzzFun,
I only know how to do this question using simultaneous equations. :oops: Could you please help to advise how to do this question in suitable method. Thank you very much.

Hi

http://www.flickr.com/photos/62167097@N02/6705370185/in/photostream

cheers.

[tianzhu]

Hi pixiedust


For your first question, there was quite a similar question discussed in one of the earlier posts.Maybe, it'll help.

The solution to your question.

1 unit ------ 1+3/4 ------7/4
4 units -------7/4*4 ------7

1 part -------- 7+3/4 ------- 31/4
4 parts -------- 31

3 parts ------- 23.25
Sally received (23.25 + 0.75) ------- 24

(Note 3/4 is equal to 0.75)

Best wishes

http://farm5.staticflickr.com/4019/4713599224_8f586290c0_z.jpg\">

[tianzhu]

Hi pixiedust


For the second question,

First day
Male participants ------ 100% + 70
Female participants ------ 100%

Second day
Male participants ------ 80% + 56 (decreased by 20%)
Female participants ------ 110% (increased by 10%)

190% + 56 ------ 531
190% ------ 475
100% ------- 475/190 * 100 ------- 250

Number of participants for first day -------- 250 + 70 + 250 ------ 570
Number of participants for second day -------- 256 + 275 ------ 531

Total number of participants ------ 570 + 530 ------ 1101

Amount collected ------ 1101*35 ------ 38535


For the third question, you may use “Units and Parts”.If you have a copy of Challenging Maths Problems Made Easy by Ammiel Wan, please refer to the chapter on \"Changed Quantities Concept\".

At first
Jane ------- 135
Iris ------- 120

Jane gave away 1 unit (25%).
Iris gave away 4 units.

In the end
Jane ------- 2 parts
Iris ------- 1 part.

Equalise the parts so as to make comparison.

135 – 1 unit -------- 240 – 8 units
7 units ------- 105
1 unit ------- 15

Iris gave away (4*15) or 60 sweets.

Jane had (135 – 15) or 120 sweets in the end.

Best wishes