This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Thursday, March 06, 2008

### Red Swastika School P5 CA1 2008 Math Paper 2 (Q13)

In a Maths quiz, each pupil had to answer 20 questions. 5 points were given for each correct answer and 2 points were taken away from each wrong answer. Mirabel answered all questions and scored 79 points. How many questions did she answer correctly?

Solution

Right answer ----- plus 5 points

Wrong answer ----- deduct 2 points

Difference between right and wrong ----- 7 points

Assuming that Mirabel had all 20 questions right, she would have -----

20 questions x 5 points = 100 points

However, she had only 79 points, which means -----

100 points – 79 points = 21 points

She “lost” 21 points.

7 “lost points” ----- 1 (question wrong)

1 “lost point” ----- 1/7

21 “lost points” ----- 1/7 x 21 = 3 (questions wrong)

20 – 3 = 17

keentolearn said...

Dear Mr Song

Will appreciate it if could post some similar types of questions from your database which can help to solve the following problems

1) There are 85 plates of duck rice for 80 people. Each adult eats 2 plate of duck rice and every three children share 1 plate of duck rice. How many adults and children are there?

2) 20 boys and girls sold tickets for a concert. Each ticket was sold at \$5.Each boy sold 5 tickets and each girl sold 3 tickets. The amount collected by the boys was \$20 more than the amount collected by the girls. Find a) how many girls were there in the group b) how many tickets were sold altogether?

Excel Eduservice said...

Keentolearn,

My apologies, but due to our busy schedule, we have stopped working problem sums for the public.

keentolearn said...

Dear Mr Song

I understand that, but if you have similar types of questions from your current database,will appreciate it very much if could help.

Excel Eduservice said...

Point noted. Will alert you if another such question is posted.

Observer said...

Ans to Q1.
A + C --> 80
2 A + 2 C --> 160

2 x A + 1 x (C / 3) --> 85

(5/3) C --> 160 - 85 = 75
C --> (3/5) x 75 = 45

A --> 80 - 45 = 35

There are 35 adults and 45 children.

Ans to Q2.

B + G --> 20
5 B + 5 G --> 100

\$5 x (5 x B - 3 x G) --> \$20
5 B - 3 G --> 4

8 G --> 100 - 4 = 96
G --> 12

B --> 20 - 12 = 8

5 x 8 + 3 x 12 = 76 tickets

76 tickets were sold altogether.

keentolearn said...

Dear Mr Song

You may wish to take another look at these problems again.Other than Algebra and Guess and Check, are there other more efficient way?

Best Wishes

Excel Eduservice said...

At this moment I am still quite tied down. PSLE is over but have to concentrate on P4s and P5s for now.

Will try to get back to you soon.

Excel Eduservice said...

Very quickly, here is solution for Q1. Will get back to you on Q2 when time permits.
Q1 –
1 child ----- 1/3 plate
Diff between 1 adult and 1 child ---- 5/3 plates
Therefore for every 1 adult in place of 1 child ---- 5/3 ‘extra plate’

Assume all children ----- 80 ppl x 1/3 = 80/3 plates
But there 85 plates ----- 255/3 plates
Which means ----- 255/3 – 80/3 = 175/3 ‘extra plates’

5/3 ‘extra plates’ ----- 1 adult in place of 1 child
1/3 ‘extra plate’---- 1/5
175/3 ‘extra plates’----- 175 x 1/5 = 35 (adults)
Children ----- 80 – 35 = 45 (children)

Excel Eduservice said...

Q2 –
(a)
1 boy ---- 5 tickets x \$5 = \$25
1 girl ----- 3 tickets x \$5 =\$15

For every girl that sells in place of 1 boy, the difference between the sales of girls and boys is increased by---- \$25 + \$15 = \$40 ** (girls sell \$15 more, boys sell \$25 less)

If 10 girls and boys ---
10 girls ---- 10 girls x \$15 = \$150
10 boys --- 10 boys x \$25 = \$250
Which means boys would have sold \$100 more than girls.

For boys to be \$20 more than girls, girls must close the difference in sales by
----- \$100 - \$20 = \$80

** 1 girl in place of 1 boy ---- \$40
2 girls in place of 2 boys ---- \$80

2 girls more ----- 10 + 2 = 12 girls (Ans for a)

Working for (b) should not be a problem for you.

Right, have to get back to our P4 and P5 students’ work. Still very busy.

keentolearn said...

Dear Mr Song

Anonymous said...

Dear Sir,

On my personal note, i find that your working is very long winded and quite confusing too.

The confusing part is where you express the plates into fraction which i find very illogical.

How can divide a plate into so many fracton to share with people?

Thanks
Confused

MathsGeek said...

There are 85 plates of duck rice for 80 people. Each adult eats 2 plate of duck rice and every three children share 1 plate of duck rice. How many adults and children are there?

This can be solved by making supposition.

Solution:

Suppose that all the 80 people are adults.

80 adults ----> 80 * 2
= 160 plates

*However, the question stated that there are 85 plates for adults.

160 - 85 = 75 plates for the children

1 plate ----> 3 children
75 plates ---> 75 * 3
= 225 plates

Difference = (2 plates + 3 plates = 5 plates

225/5 = 45 children

= 35

MathsGeek said...

20 boys and girls sold tickets for a concert. Each ticket was sold at \$5.Each boy sold 5 tickets and each girl sold 3 tickets. The amount collected by the boys was \$20 more than the amount collected by the girls. Find a) how many girls were there in the group b) how many tickets were sold altogether?

This question can be solved by supposition method.

Solution:

Suppose there are 20 boys.

20 * 5 * \$5 = \$500

Boys = \$ 20 more

\$500 - \$20 = \$480

Girls = \$480

Difference = 5 * \$5 + \$3 * 5
= \$40

Number of girls = \$480/\$40
= 12 girls

You may continue to solve part (b)

MathsGeek said...

Another way of solving this is to express all to girls

Solution:

Suppose there are 20 girls.

20 * 3 * \$5 = \$300

Boys = \$20 more

Boys = \$300 + \$20
= \$320

Difference = 5 * \$5 + 3 * %5
= \$40

Number of boys = \$320/\$40
= 8

Number of girls = 20 - 8
= 12

So! which method do you prefer?

keentolearn said...

Dear MathsGeek

Thank you

keentolearn said...

Dear MathsGeek

Thank you

MathsGeek said...

Keentolearn!,

You are most welcome. I like to help students who have difficulties in solving mathematics.

keentolearn said...

Dear Mathsgeek

1 plate ----> 3 children
75 plates ---> 75 * 3
= 225 plates

Why is Difference = (2 plates + 3 plates = 5 plates ?

keentolearn said...

Dear Mathsgeek

Also why 75 plates ---- 225 plates when 1 plate --- 3 children

MathsGeek said...

Dear Keentolearn!,

Thanks for pointing out my mistake...This shows that you have a good observation and are really keen to learn.

1 plate ----> 3 children
75 plates ----> 3 * 75
= 225 children*

*It is impossible to have 225 children since the number of people is 80 but this is just an assumption.

1 child (difference) ----> 2* 1 plate + 3 * 1 plate = 5 plates

**Logic - since every 3 children share 1 plates, the number of children who share 225 plates should be less.

5 plates (difference) ----> 1 child

225 plates (difference) ----> (225 * 1) / 5 = 45 children

Adults = 80 - 45 = 35

If you have difficulties understanding my solution, my advice to you is you should follow Mr Song method.

Thanks

Doubtful said...

Hi!,

A shop sells stools with three, four or five legs. There are 112 stools for sale. The total number of legs for all these stools is 425. The total number of three-legged and four-legged stools is 3 times the number of five-legged stools. How many three-legged stools are there?

Seriously speaking...the phrasing of english is confusing...

Thanks

MathsGeek said...

Dear Doubtful!,

Below is the question that you have asked.

A shop sells stools with three, four or five legs. There are 112 stools for sale. The total number of legs for all these stools is 425. The total number of three-legged and four-legged stools is 3 times the number of five-legged stools. How many three-legged stools are there?

Below is my solution.

4 units -----> 112 stools
1 unit -----> 112/4
= 28 stools of five-legged

112 - 28 = 84 stools of three and four-legged

No. of five-legged stools = 28 * 5
= 140 legs

425 - 140 = 285 legs *

*Note - These 285 legs belong to the three and four-legged stools

Suppose all the 84 stools are four-legged stools.

84 * 4 = 336 legs

There should be 336 legs of four-legged stools but base on the working above, there are only 285 legs of three and four-legged stools.

336 - 285 = 51 legs of three-legged stools

51/3 = 17 stools of three-legged stools

Therefore, there are 17 three-legged stools.

Check: Total stools = 112
No of Three-legged = 17
No of four-legged = 84 - 17
= 67

Total no of three and four-legged stools = 67 + 17 = 84

The total number of three and four-legged stool is 3 times the number of five-legged stools, which is 28 (84/3)

As such, the total number of stool should be : 84 + 28 = 112 stools.

That was tough and tedious...

Thanks

AnointedOne said...

MathsGeek!,

I think there is an error in your working. Although the number of stools seems to add up, the number of legs seems to differ....

Thanks

Anonymous said...

Yes anointedone is right.

4units = 112
1unit = 28
There are 28 five-legged stools
3units = 3 x 28 =84
(There are 84 three-legged and four-legged stools)

28 x 5 = 140 legs

425 - 140 = 285
(balance 285 legs belong to 3 legged & 4 legged stools)
84 x 3 =252

285 -252 = 33

84 - 33 = 51

There are 51 three-legged stools & 33 four-legged stools

Anonymous said...

A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?

MathsGeek said...

Hi Anonymous!

A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?

This question is not uncommon and is not something new either.
This question can be solve base on the following methods:

1) Guess and Check method - This method is time-consuming and tedious and strongly recommended.

2) Algebra - This is a great toolin solving all mathematical problem but at P6 level, students are not expose to using letters to solve since they have been learning only basic ones.

3) Supposition method - This is strongly recommended.

Solution: Supposition method

Suppose all the 40 pupils are boys >.

40 * 3 = 120 stacks of newspapers

Number of stacks of numberspapers carry by girls:

120 - 30 = 90 stacks of newspapers

Difference = 3 + 2
= 5

No. of girls = 90 / 5
= 18

No of boys = 40 - 18
= 22

Ratio : Boys : Girls
22 : 18
11 : 9

Check : Boys = 22 * 3
= 66 stacks
Girls = 18 * 2
= 36
Difference(boys) = 66 - 36
= 30 more

MathsGeek said...

Hi Anonymous!

A class of 40 pupils helped to carry bundles of old newspapers in an event organised to collect funds for the old folks. Each boy carried 3 stacks of newspapers and each girl carried 2 stacks. Altogether, the boys carried 30 more stacks than the girls. What is the ratio of the number of boys to the number of girls in the class?

Note: Apologies. Please ignore my previous thread. There are some erroneous in my solutions. I have make further amendments in my working. Please spare some time to read and digest.

The above question is not uncommon and is not something new either.
This question can be solved base on the following methods:

1) Guess and Check method - This method is time-consuming and tedious and not strongly recommended.

2) Algebra - This is a great tool in solving all mathematical problem but at P6 level, students are not expose to using letters to solve since they have been learning only basic ones.

3) Supposition method - This is simpy and concise and is strongly recommended.

PS: Supposition method can be expressed and shown in two ways.

Solution: 1) Supposition method

Suppose all the 40 pupils are boys.

40 * 3 = 120 stacks of newspapers

Number of stacks of numberspapers carry by girls:

120 - 30 = 90 stacks of newspapers

Difference = 3 + 2
= 5

No. of girls = 90 / 5
= 18

No of boys = 40 - 18
= 22

Ratio : Boys : Girls
22 : 18
11 : 9

Check : Boys = 22 * 3
= 66 stacks
Girls = 18 * 2
= 36
Difference(boys) = 66 - 36
= 30 more

Solution: 2) Supposition method

Suppose all the 40 pupils are girls.

Suppose that all the 40 pupils are girls

40 * 2 = 80 stacks carry by all girls

Boys = 30 more stacks

Boys = 80 + 30
= 110 stacks

Difference = 3 + 2
= 5

No. of boys = 110 / 5
= 22

No. of girls = 40 - 22
= 18

Ratio: Boys : Girls
22 : 18
11 : 9

Check : Boys = 22 * 3
= 66 stacks
Girls = 18 * 2
= 36
Difference(boys) = 66 - 36
= 30 more

Do you think the above method is useful and easy compare to guess and check?

Thanks

Anonymous said...

Hi, MathsGeek

Thank you.

Please explain how do you get

Difference = 3 + 2
= 5

MathsGeek said...

Hi Anonymous!,

Using tabulation and guess and check to derive an analysis below.

-----------------------------------
boys stacks girls stacks differing
-----------------------------------

20 20*3 20 20*2 60-40=20
= 60 = 40

21 21*3 19 19*2 63-38=25
= 63 = 38

22 22*3 18 18*2 66-36=30

-----------------------------------
Explanation: Notice that for every 1 increase in boys leads to an increase of stacks by 3. For every decrease in 1 girl will lead to a decrease of 2 stacks.

Therefore, every increase of 3 stacks by boys and every decrease of 2 stacks by girls will lead to a difference of 5.

Take note of the difference. What did you see base on your observation. Notice that the resulted difference is increase by 5. This is the result of the increase of every 3 stacks by boys and the decrease of every 2 stacks by girls.

Hope that i have help to clarify your doubts.

MathsGeek said...

Hi Anonymous!,

Note: Apologies, this is missing figures. No worries, I have make the necessary amendments.

Using tabulation and guess and check, i have derived an analysis below.

-----------------------------------
boys stacks girls stacks differing
-----------------------------------

20 20*3 20 20*2 60-40=20
= 60 = 40

21 21*3 19 19*2 63-38=25
= 63 = 38

22 22*3 18 18*2 66-36=30
= 66 = 36

-----------------------------------
Explanation: Notice that for every 1 increase in boys leads to an increase of stacks by 3. For every decrease in 1 girl will lead to a decrease of 2 stacks.

Therefore, every increase of 3 stacks by boys and every decrease of 2 stacks by girls will lead to a difference of 5.

Take note of the difference. What did you see base on your observation. Notice that the resulted difference is increase by 5. This is the result of the increase of every 3 stacks by boys and the decrease of every 2 stacks by girls.

Hope that i have help to clarify your doubts

Cheers :)

Logic said...

Anonymous!,

Your solution for the number of three,four or five-legged stools seems wrong.

Although the total number of stools and the total number of legs tend to add up, your last working seems to have error.

Below is an extract of your working. Mistake is highlighted in bold.

4units = 112
1unit = 28
There are 28 five-legged stools
3units = 3 x 28 =84
(There are 84 three-legged and four-legged stools)

28 x 5 = 140 legs

425 - 140 = 285
(balance 285 legs belong to 3 legged & 4 legged stools)
84 x 3 =252

285 -252 = 33

84 - 33 = 51

Note: 84 refers to the number of stools not the legs.

since 285 legs - 252 legs = 51 legs but not the number of stools.

It is quite illogical to minus the number of legs from the number of stools. It does not make any sense.

Confused

Worried said...

Dear Mr Song and all,

I agreed with "Logic" that there are errors for the last working.

84 - 33 = 51

Seriously speaking, i do not understand why "anonymous" use the number of stools which is 84 minus the number of legs, which is 33. It does not sound feasible.