Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

Hi Mathsguru,


Need your help with the 2 questions below :

1) Mrs Yee had 60% more books than Mdm Ling. Miss Tang had 25% fewer books than Mrs Yee. Mrs Yee and Mdm Ling gave Miss Tang some books in the ratio of 3 : 1. As a result, Miss Tang had 1 1/2 times as many books as before. Given that Mrs Yee had 240 more books than Mdm Ling in the end, how many books did Mrs Yee give to Miss Tang ?

I tried solving the question and got the answer = 90, is it correct ?

2) In the figure below not drawn to scale, the area of the triangle is 250% of the area of the rectangle. The unshaded part of the triangle is 300% of the unshaded part of the rectangle. Find the area of the shaded part if the area of the rectangle is 64 cm2.

http://www.postimage.org/image.php?v=gxDpur

Thank you so much!

[mathsguru]

firebird:

Dear Mathsguru


Good evening.

Please help me on the following P6 maths:

1) If Ahmad and Ben work together, they can compete a job in 12 days. If Ahmad and Ben worked together for 3 days, followed by Ben who worked alone for the next 5 days, they can finish 5/12(fraction) of the job. How many days will each of them need to complete the job if they work alone?

2) Allyson, Betty and Charlene shared to buy a watch for their father. Allyson paid 1/4(fraction) of the total share of Betty and Charlene. Betty paid 1/5 (fracion) the total share of Allyson and Charlene. If Charlene paid $56 more than Betty, how much did the watch cost?

Many thanks
firebird

Hi Firebird,

Here are my solutions. Hope they help!


MathsGuru

http://www.postimage.org/image.php?v=PqIghoS

http://www.postimage.org/image.php?v=PqIgrnr

[mathsguru]

firebird:

Dear Mathsguru


Good morning.

Please help me on the following P6 math:

1) Ali and Bala had a total of 1134 marbels. After each of them had given away some marbles, the number of marbles Ali has was 4 times the number of marbles he had given away and the number of marbles Bala had was 3 times the number of marbles he had given away. They had a total of 897 marbles left. How many marbles did Bala had first?

My working via simultaneous equation a) 5 Ali + 4 Bala = 1,134
b) 4 Ali + 3 Bala = 897 and c) Subtracting b from a is 1 Ali + 1 Bala =237
MY ANSWER IS 204 FOR BALA (which was the given answer).

Please let me know:
(i) Is simultaneous equation method to find solution allowed for PSLE?
(ii) How to find the solution based on model mehtod for the question 1.


Thank you.
firebird

Hi Firebird,

In my opinion, I think it's the extent in which the simultaneous equations are being applied. It may be confusing for a P6 student to understand simultaneous equations in pure algrabraic sense as they have only learnt basic algebra in P6. However, for this question, what you've done is actually a very simple form of applying simultaneous equations, which is definitely acceptable! Diagrams/models are not necessary, but are good for visualisation, in case the student cannot \"see\" what minus what or what plus what.

Here's my solution anyway.

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=PqIi199

[mathsguru]

YLH88:

Hi Mathsguru,


Need your help with the 2 questions below :

1) Mrs Yee had 60% more books than Mdm Ling. Miss Tang had 25% fewer books than Mrs Yee. Mrs Yee and Mdm Ling gave Miss Tang some books in the ratio of 3 : 1. As a result, Miss Tang had 1 1/2 times as many books as before. Given that Mrs Yee had 240 more books than Mdm Ling in the end, how many books did Mrs Yee give to Miss Tang ?

I tried solving the question and got the answer = 90, is it correct ?

2) In the figure below not drawn to scale, the area of the triangle is 250% of the area of the rectangle. The unshaded part of the triangle is 300% of the unshaded part of the rectangle. Find the area of the shaded part if the area of the rectangle is 64 cm2.

http://www.postimage.org/image.php?v=gxDpur

Thank you so much!

Hi YLH88,

Here are my solutions. I didn't get 90 books for the 1st question. Perhaps you take a look at my solution and see if my understanding of the question is right? I double-checked my answer...think it should be correct.

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=TsjhX9

http://www.postimage.org/image.php?v=aVtw09r

[firebird]

Dear Mathsguru


Good morning.

Please help me on the P6 maths:

1) What is the value of 18- 6 + 2 x 5?

My working is 2 x 5 equal 10
6 + 10 equal 16
18 - 16 equal 4

However, the given answer was 22.
My understanding was to follow this sequence:
division, multipilication, addtion and substraction. Please correct me.

2) Given 21 boxes. The 1st has 3 marbles, 2nd box has 6 marbles, 3rd box has 9 marbles and so on in this pattern. What is the total number marbles in all the 21 boxes?

By adding one by one I can get answer 693

My request is: any short cut as this is a 1 mark question?

Many thanks
firebird

[YLH88]

Hi Mathsguru,


I’m definitely sure your answer is correct But need you to help explain some queries :

For Qn 1 on the books, why do we need to break the 1 big unit into 4 units ? I thought 3 : 1 is referring to the original units where Mrs Yee has 6 units (160%) and Mdm Ling has 5 units (100%) ?

For Qn 2 on the diagram, 160 - shaded area = 3 x (64 - shaded area), multiple by 3 is it because of the unshaded triangle is 300% of the unshaded rectangle ?

Thank you very much !

[Dharma]

firebird:

Dear Mathsguru


Good morning.

Please help me on the P6 maths:

1) What is the value of 18- 6 + 2 x 5?

My working is 2 x 5 equal 10
6 + 10 equal 16
18 - 16 equal 4

However, the given answer was 22.
My understanding was to follow this sequence:
division, multipilication, addtion and substraction. Please correct me.

2) Given 21 boxes. The 1st has 3 marbles, 2nd box has 6 marbles, 3rd box has 9 marbles and so on in this pattern. What is the total number marbles in all the 21 boxes?

By adding one by one I can get answer 693

My request is: any short cut as this is a 1 mark question?

Many thanks
firebird

Q1
Your 2nd step should be … (-6 + 10 = 4; then 18 + 4 = 22)

Q2

Box 1 – 3
Box 2 – 6
Box 3 – 9
Box N – 3N

So, Box 21 – 63 marbles

Total marbles in 21 boxes
= 3 + 6 + 9 + …+ 60 + 63
= 3(1 + 2 + … + 20 + 21)
= 3 x (21 x 22/2)
= 693


http://www.postimage.org/image.php?v=Ts1pF0r

[Thein]

hi firebird

for question 2
sum of arithmetic progression
s= n/2(2a+(n-1)d)
where
s = sum of progression
n = number of terms
a = value of first term
d = difference between 2 terms
hence
s=21/2(2*3 +(21-1)3)
= 21/2(6+60)
=21/2(66)
=2133
=693
hope i am correct.

[firebird]

Dear Dharma


Many thanks. You have guided me very well.

I also thank to mathsguru and all.

Best regards
firebird

[mathsguru]

firebird:

Dear Mathsguru


Good morning.

Please help me on the P6 maths:

1) What is the value of 18- 6 + 2 x 5?

My working is 2 x 5 equal 10
6 + 10 equal 16
18 - 16 equal 4

However, the given answer was 22.
My understanding was to follow this sequence:
division, multipilication, addtion and substraction. Please correct me.

2) Given 21 boxes. The 1st has 3 marbles, 2nd box has 6 marbles, 3rd box has 9 marbles and so on in this pattern. What is the total number marbles in all the 21 boxes?

By adding one by one I can get answer 693

My request is: any short cut as this is a 1 mark question?

Many thanks
firebird

Hi Firebird,

1) The order of operations should be BODMAS --> Brackets, Orders, Division AND Multiplication, Addition AND Subtraction.
Note that I highlighted the word \"AND\" for Division/Multiplication and Addition/Subtraction, because Division & Multiplication are of the same \"rank\" and Addition & Subtraction are of the least priority but same rank.

Hence, for this question: 18- 6 + 2 x 5, we should do multiplication 1st since there are no brackets and there is only 1 multiplication. We'll obtain 18- 6 + 10. Next, because Addition & Subtraction are of the same rank, we do from left to right: 12 + 10 = 22.

With more practice, your child should be able to get a hang of the order of operations. It is very very important, so must try to master this asap!



2) For this question, the number pattern is 3, 6, 9, 12, etc --> multiples of 3. Although there's an arithmetic progression formula for this, I will try to explain in a more simplified manner.

As a rule of thumb, for a number pattern that involves a constant difference, the average of the pattern can be obtained by taking the average of the first and last terms.

Last term (21st box) = 3 x 21 = 63.

Average of the 21 boxes = (3 + 63) / 2 = 33.

Using the concept of average, total sum of marbles = average x total number of boxes.

Therefore, total no. of marbles = 33 x 21 = 693.

Though there are several methods out there, I would encourage your child to learn and use this method because it works on all types of number pattern as long as the difference between every 2 consecutive numbers are the same.

For instance, sum of all no.s from 1 to 99:
Average = (1 + 99) / 2 = 50.
No. of numbers = 99.
Total sum = 50 x 99 = 4950.

Best regards,
MathsGuru