Q&A - PSLE Math

[Brenda10]

Hifive:

Hi


Source : Andrew Er's New Syllabus Mathematics

A class has a total of 40 pupils. Each girl has an average mass of 40kg and each boy has an average mass of 48kg. If the total mass of the girls is 512 kg lighter than the total mass of the boys, how many girls are there in the class ?

Ans: 16 girls.

Though the book provided the solution to the question but don't quite get it and hope that parents/students here can provide alternative method of solution.

Thanks & Regards

Hi Hifive, how about using the guess and check method.


Boy Girl

20 x 48=960, 20 x 40 = 800 (Diff:160 - wrong)
22 x 48 = 1056, 18 x 40 = 720 (Diff: 336) - wrong)
24 x 48 = 1152, 16 x 40 = 640 (Diff: 512- Correct)

There are 16 girls in the class.

Thank you

[tianzhu]

Hi


Hope this helps.

Best wishes.

http://farm6.static.flickr.com/5088/5304261023_79d9af9503_b.jpg\">

[Belle2011]

Can anybody please help to solve:


In a primary school, 50 pupils were surveyed on the pets they liked. 80% of the pupils liked dogs, 50% of them liked birds and 34% of them liked rabbits. The survey results were that 1 out of every 5 pupils did not like any of the animals.
What is the least number of pupils who liked all 3 types of animals.
(model ans : 2).

Thanks.

Cheers,
Belle.

[Hifive]

Hi Brenda10 and tianzhu


Thank you for providing the alternative methods of solution. Yes, make it easier to understand now. THANKS SO MUCH!

Sorry, 2 more to go from the same book:

1. Benny spent 15% of his salary on food and $440 on camera. Then he spent 30% of the remainder on clothes and saved the rest of his salary. He found that the amount he spent on clothes was $120 more than the amount he had spent on food.
(a) How much did he spend on food? Ans: $360
(b) How much did he save? Ans: $1120


2. Wilson purchased a certain number of wallets at $6 each. If he had purchased those at $8 each, he would have purchased 20 fewer wallets. How much money did he have?
Ans : $480

Thanks again.

[tianzhu]

Hi Hifive


I'll take Q2 first, it's an interesting one.

One way to look at it to to see the relationship between the difference in number of wallets and the amount of money.

Hope this helps.

Best wishes.

http://farm6.static.flickr.com/5287/5305519560_ea03d6bc22_b.jpg\">

[Brenda10]

Hifive:

Hi Brenda10 and tianzhu


Thank you for providing the alternative methods of solution. Yes, make it easier to understand now. THANKS SO MUCH!

Sorry, 2 more to go from the same book:

2. Wilson purchased a certain number of wallets at $6 each. If he had purchased those at $8 each, he would have purchased 20 fewer wallets. How much money did he have?
Ans : $480

Thanks again.

If we use the guess and check method, then the common factor of 6 and 8 are 24, 48.

$6, $8
240/6= 40, 240/8 = 30 (diff 10 bags - wrong)
480/6= 80, 480/8 = 60 (diff 20 bags - correct)

As for the other question dd tries to solve but unable to get the answer. Hopefully Tianzhu and somebody else can help too.

Hi Hifve, would you mind to show the methods provided by the book so as we can also learn another approaching to this question.

Thank you

[tianzhu]

Brenda10:

As for the other question dd tries to solve but unable to get the answer.

Hi Brenda10

I’ll try to breakdown the question into steps for you to try again.

Start with a simple drawing.

Consider the remaining part first.

3 parts to show amount spent on food, 7 parts to show savings.
1 part is $40 more than 1 unit (represent spending on food) ( the amount he spent on clothes was $120 more than the amount he had spent on food)

We have

3 units (15% of salary)
440 + (10units+400) which is equal to 85% of salary

15% --- 3 units
5% --- 1 unit

840+10 units --- 85%

Therefore we have

840+10units ----17 units
Hence 1 unit ---- 120

a)Amount spent on food --- 3*120 --- 360

b)Amount saved --- (7*120) + (7*40) ---- 1120

Please let me know if you need more information.

Best wishes

[Brenda10]

tianzhu:

Brenda10:

As for the other question dd tries to solve but unable to get the answer.

Hi Brenda10

I’ll try to breakdown the question into steps for you to try again.

Start with a simple drawing.

Consider the remaining part first.

3 parts to show amount spent on food, 7 parts to show savings.
1 part is $40 more than I unit (represent spending on food) ( the amount he spent on clothes was $120 more than the amount he had spent on food)

We have

3 units (15% of salary)
440 + (10units+400) which is equal to 85% of salary

15% --- 3 units
5% --- 1 unit

840+10 units --- 85%

Therefore we have

840+10units ----17 units
Hence 1 unit ---- 120

a)Amount spent on food --- 3*120 --- 360

b)Amount saved --- (7*120) + (7*40) ---- 1120

Please let me know if you need more information.

Best wishes

Hi Tianzhu

Thank you very much.

DD said she can understand now.

Have a nice day.

[Hifive]

Hi tianzhu and Brenda10


Thank you for the explanation and solution. Really helps in my understanding.

Brenda10:

Hi Hifve, would you mind to show the methods provided by the book so as we can also learn another approaching to this question.

Thank you

Brenda10

The book solution to (those in blue font)

1. Benny spent 15% of his salary on food and $440 on camera. Then he spent 30% of the remainder on clothes and saved the rest of his salary. He found that the amount he spent on clothes was $120 more than the amount he had spent on food.
(a) How much did he spend on food? Ans: $360
(b) How much did he save? Ans: $1120

a) 3 units === 15% + $120
1 unit ==== 5% + $40
10 units === 50% + $400
15% + $440 + 50% + $400 === 100%
100% === 65% + $840
35% === $840
1% === 840 / 35 = $24
15% === 15 x 24 = $360

b) 50% + $400 = ($50 x 24) + $400
= $1600
70/100 x $1600 = $1120

2. Wilson purchased a certain number of wallets at $6 each. If he had purchased those at $8 each, he would have purchased 20 fewer wallets. How much money did he have?

20 x $6 = $120
$120/$2 = 60 wallets
60 x $8 = $480


I can now understand the book's 1st solution better after going thru' tianzhu's solution. As for the 2nd question, I can solve now using tianzhu and Brenda10's explanation. Thanks so much to both of you.

Cheers

[Brenda10]

Hifive:

Brenda10


The book solution to (those in blue font)

a) 3 units === 15% + $120
1 unit ==== 5% + $40
10 units === 50% + $400
15% + $440 + 50% + $400 === 100%
100% === 65% + $840
35% === $840
1% === 840 / 35 = $24
15% === 15 x 24 = $360

b) 50% + $400 = ($50 x 24) + $400
= $1600
70/100 x $1600 = $1120

Cheers

Hi Hifive

Thank you for providing the solution.