Q&A - PSLE Math

[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.

[tianzhu]

Hi Brenda10 and Hifive


Good Morning

You’re welcome.

Wishing you a fabulous and prosperous 2011.

Good cheers, good health and good PSLE results.

Best wishes

[tianzhu]

Belle2011:

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).

Hi Belle2011

Good Morning

Number of pupils who did not like any of the animals -----1/5*50 ----- 10
Number of pupils who like any of the animals -------40 (50-10)

Number of pupils who like dogs ------ 40 (80%)

Number of pupils who like birds ------ 25 (50%)

Number of pupils who like rabbits ------ 17 (34%)

The tricky part starts from here; I think one needs to have some knowledge about Set notation and Venn diagram to be able to understand the steps better.Therefore, I am not sure if your question is within PSLE syllabus.

As calculated earlier, the number of pupils who like any of the animals is 40. However 40+25+17 adds up to 82.

Here a Venn diagram will come in handy.

25+17 --- 42
42-40 --- 2

If you draw a Venn diagram, you’ll see that the number of pupils who like dogs and birds is equal to 23 and the number of pupils who like dogs and rabbits is equal to 15 and the number of pupils who like all three types of animals is 2.This adds up to 40.

Wishing you a fabulous and prosperous 2011.

Good cheers, good health and good PSLE results.

Best wishes

PS --- You may follow these links to learn more about Venn diagram.

http://www.youtube.com/watch?v=nf-pnW_wVRw&feature=related

http://www.youtube.com/watch?v=mMh0QdPHTRM&feature=related

[Belle2011]

Dear tianzhu,

Thanks very much for your help.

Cheers,
Belle.