Tutor MathsGuru: Ask me for your burning Maths questions!

[CoffeeCat]

oh yea i underestimated the question.

i think i know how the setter got his 360.

Due to the complexity of this question we shall break it up into 2 parts, the initial cutting and the subsequent cuttings

first notice that only 3 divides 90 evenly, and 50/3 = 16 r2 , 70/3=23 r1,
2 divides 50 and 70 and 90 evenly while 90, 70 & 50 leave a remainder of 2 upon division by 4.

initial cutting
if we divide 70 by 3, we will be left with an unuseable wastage of 1*50*90, too large so we will rule this out.

For the rest of the configurations, we will be left with wastages with 1 side of 2cm long, which will be dealt with in the subsequent cutting part.

Intuitively this might be the most efficient because wastage is confined to only 1 side of the block.
Let's say we only want to create wastage along 1 side, the only 2 configurations are (3 will have to divides into 90)
a) (90/3) & (70/2) & (50/4)
The initial cutting yields (30 * 35 * 12)=12600 cuboids
and we are left with a 2*70*90 board.
This will yield either 506 or 510 additional cuboids.
Total = 13106 or 13100 cuboids, leaving 600 cubic cm wastage for 13100 cuboids..

b) (90/3) & (50/2) & (70/4)
The initial cutting yields (30*25*17)=12750 cuboids
and left with a 2*50*90 board.
which will yield either 352 or 360 additional cuboids.
therefore wastage is 360 cubic cm for 13110 cuboids (this is the configuration the setter is looking for)

Lets say we end up creating wastage along 2 sides after the initial cutting.
then there are only 2 more cases to consider (when 3 divides into 50)
a) (50/3) & (90/4) & (70/2)
b) (50/3) & (70/4) & (90/2)


Maybe you can share how you got your 180 wastage.

[Dharma]

firebird:

Dear coffeeCat & Dharma


Thanks for your reply.

The question one answer given by coffeecat is not as the same as the given answer - i.e. 360 cm3. I really do not know!

The question two answer given by Dharma is same as given answer - i.e 6.17am. However, I could not understand the working.

Regards
firebird

Hi firebird,

Q2
2000 hrs + 1990 mins + 1980 sec
= 2000 + (1990 x 60 + 1980)/3600
= (2000 + 33 + 43/60) hrs
= (1992 + 8 + 24 + 9 + 43/60)hrs
= 84 days + 17hrs + 43/60 hrs

84 days before midnight is also midnight. So, we left with 17 hrs and 43 mins before midnight.

Time is 17 hrs and 43 mins before midnight i.e. 6.17am

[OngMum]

Thank you, Tang for the link on the correct qns phrasing.

Thank you, Mathsguru for the problems solving.

Have a good day!

Cheers!

[YLH88]

Hi Mathsguru,


Thank you for the solution!

Regards

[firebird]

Dear Coffeecat and Dharma


Thank you for the answer.

1) Coffeecat, for the block question, I got the answer 180 = 90 x 2 x 1
Your working is rather too tough for me to follow. Neverheless, I will try again and again until this weekend - 29/3/10. If sill lost, I will ask for help.

2) Dharma, I was able to follow your working for the time quesion on a second attempt.

Many thanks.

Regards
firebird

[Dharma]

firebird:

Dear Coffeecat and Dharma


Thank you for the answer.

1) Coffeecat, for the block question, I got the answer 180 = 90 x 2 x 1
Your working is rather too tough for me to follow. Neverheless, I will try again and again until this weekend - 29/3/10. If sill lost, I will ask for help.

2) Dharma, I was able to follow your working for the time quesion on a second attempt.

Many thanks.


Regards
firebird

Hi firebird,

Coffeecat has given you a detailed explanation considering the different cases. I’ll just try to simply his explanation and hopefully you can follow.

90 divide by 3 = 30
50 divide by 2 = 25
70 divide by 4 = 17R2 (You are left with remainder of 2cm uncut)

If u cut the 50cm x 70cm x 90cm in such a way where little cuboid of side 3cm is along the 90cm of the block, 2cm side of little cuboid along the 50cm of the block and 4cm side of the little cuboid is along the 70cm of the block.

Total no. of small cuboids cut-out = 30 x 25 x 17 = 12,750
Total volume of cuboids cut-out = 12,750 x (2 x 3 x 4)cm3 = 306,000cm3

Volume of block left = (50 x 70 x 90)cm3 – 306,000cm3 = 9000cm3

OR

Volume left = 90cm x 50cm x 2cm = 9000cm3

You will realize that after cutting off the little cuboids, you are left with a block of 90cm x 50cm x 2cm. We cut this block again into smaller cuboids of 2cm x 3cm x 4cm.

90 divide by 3 = 30
50 divide by 4 = 12R2 (You are left with remainder of 2cm uncut)

No. of small cuboids cut-out = 30 x 12 x 1 = 360
Volume of cuboids cut-out = 360 x (2 x 3 x 4) cm3 = 8640cm3

Amount/volume of wasted wood = 9000cm3 – 8640cm3 = 360cm3

OR
Volume left/wasted = 90cm x 2cm x 2cm = 360cm3

[tianzhu]

Hi firebird


At first glance, this question may look ordinary.But it may not be so.

To minimize wastage, you need to cut out the maximum number of little cuboids.

Hope this helps.

Best wishes


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[firebird]

Dear Coffeecat, Dharma & Tianzhu


I thank you very much for the detailed explaination and working posted for the block question.

With best regards
firebird

[firebird]

Dear mathsguru


Please help me on the following P6 maths:

1) Sophie and Rachel share blue ribbons in the ratio of 5 : 2.
They want to buy some red ribbons so that the total number of ribbons they have will be tripled. In what ratio must they divide the red ribbons so that Rachel will have twice the number of ribbons she has now?

I got 17:4. But the given answer is 6:1.

2) Faizal has a rod. He needs 6 minutes to saw it into 4 pieces. How many minutes does he need to saw the rod into 28 pieces?

I got 42 minutes. But the given answer is 54 minutes

3) Customers were given a free CD for every 2 CDs they buy at a sale.
Ben spent $K and got 30CDs in all. WHat is the price of 1 CD?

I got $K/20. But the given answer is $K/10

4) There were some horses and people on a farm. There were 62 more legs than heads. There were 26 more heads than tails.

a) How many people were there?
b) How many horses were there?

I really do not know where to start for question 4 a) & b)

5) Sugar and water are mixed in the ratio 1:5 to make syrup. The volume of the syrup is 800 cm3.

a) Find the volume of sugar in the syrup.
b) Find the volume of water in the syrup.
c) How much more sugar must be added to the surup so that the ratio of the sugar to water in the syrup becomes 1:3?


a) I got 133 1/3 Cm3 But given answer 13 1/3 CM3. I hope i am right.
b) I got 666 2/3 cm3 and the given answer also 666 2/3 cm3.
c) I got 1,866 2/3 cm3 But the given answer 88 8/9 cm3


Many thanks
firebird

[Vanilla Cake]

YLH88:

[quote]Hi YLH88,

While waiting for Mathsguru's model solution, pls see whether mine using ratio is of any use or not?

(a)
D : T
8 : 11
16 : 22

D : T
19 : 19

(16+22)÷2=19

3u=18
u=6
6u=36

At first, Thomas had 36 more game cards than Doran.

(b)
D : T
19:19
38: 38

D : T
3 : 1
57:19

6u=18 [from part (a) ie 6u=36, reduce half of 36 = 18 since 19:19 has been doubled to 38:38 in part (b)]
u=3
19u = 57
Thomas lost 57 more cards to Doran.

Hi Vanilla Cake,

For (a), I got the answer using the model method. For the unit method, why did you change 8:11 to 16:22 ? Why do we multiple by 2 and not 3 or 4 etc ?

For (b), why do you change from 19:19 to 38:38 and 3:1 to 57:19 ?

Thank you![/quote]Hi YLH88,
Sorry for the late reply due to my busy schoolwork.
This is a 4-mark question is from Nanyang 2009 P6 SA1 Paper 2 Q12.

(a) You need to multiply 8:11 by 2 to get 16:22.Add 16+22=38 which is the same as 19+19=38.
(b)19:19 multiply by 2 to get 38:38 so that 38+38=76. And 3:1 multiply by 19 to get 57:19 so that 57+19=76.