Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

Hi Vanilla Cake, Dharma,


Thank you for the explanation!!

Have a good day

[Vanilla Cake]

Dharma:

abc_parent:

Q3) A set of dictionaries which fitted exactly 4 shelves, each 2.05m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of books between the two sets?


Answer: 120 dictionaries

Total thickness of dictionaries = 4 x 205cm = 820cm

Each shelf will have 205cm/5cm = 41 new dictionaries

No. old dictionaries that were replaced by the new set per row = (41/4) x 7 = 287/4 = 71.75

Only 71 old dictionaries fit into each row of the shelf.
Total number of old dictionaries = 4 x 71 = 284
Total number of new dictionaries = 4 x 41 = 164

Difference in the number of dictionaries = 284 – 164 = 120

(You cannot tear off a portion of a dictionary to force it into a shelf !!!)

Dear Dharma,
Could you pls revisit this dictionaries problem sum again? Below is the comments made by a member in another forum:

The difference is in the understanding on the layout of the shelves. You have assumed the shelves are stacked vertical, perhaps in a book case. Where as, in http://www.postimage.org/image.php?v=Tsqkvjr interpretation the shelves would be placed horizontally side by side creating one 'super' shelf of 820cm in length.

Using your approach, vertical, there is no solution as we cannot take a fraction of a dictionary - ie 71.75 dictionaries. However, using the approach that the shelves are placed side by side we have ...
- 4 shelves x 205 cm = 820cm
- at end can fit 820/5 --> 164 dictionaries
- 164 is 164/4 = 41 sets
- 41 sets x 7 = 287 old dictionaries
- difference is 287 - 164 = 123

The difference in the number of dictionaries between the two sets is 123.

This 5-mark question was from Singapore Chinese Girls' School 2009 P6 SA1 Maths paper 2 Q17 and the worksheet's answer was 120.Hope to have comments/interpretations from other members in this forum about this dictionaries problem sum on whether the shelves are stacked vertical or placed horizontally side by side etc.

Submitted by VC's mum

[Dharma]

Vanilla Cake:

Dharma:

[quote=\"abc_parent\"]Q3) A set of dictionaries which fitted exactly 4 shelves, each 2.05m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of books between the two sets?


Answer: 120 dictionaries

Total thickness of dictionaries = 4 x 205cm = 820cm

Each shelf will have 205cm/5cm = 41 new dictionaries

No. old dictionaries that were replaced by the new set per row = (41/4) x 7 = 287/4 = 71.75

Only 71 old dictionaries fit into each row of the shelf.
Total number of old dictionaries = 4 x 71 = 284
Total number of new dictionaries = 4 x 41 = 164

Difference in the number of dictionaries = 284 – 164 = 120

(You cannot tear off a portion of a dictionary to force it into a shelf !!!)

Dear Dharma,
Could you pls revisit this dictionaries problem sum again? Below is the comments made by a member in another forum:

The difference is in the understanding on the layout of the shelves. You have assumed the shelves are stacked vertical, perhaps in a book case. Where as, in http://www.postimage.org/image.php?v=Tsqkvjr interpretation the shelves would be placed horizontally side by side creating one 'super' shelf of 820cm in length.

Using your approach, vertical, there is no solution as we cannot take a fraction of a dictionary - ie 71.75 dictionaries. However, using the approach that the shelves are placed side by side we have ...
- 4 shelves x 205 cm = 820cm
- at end can fit 820/5 --> 164 dictionaries
- 164 is 164/4 = 41 sets
- 41 sets x 7 = 287 old dictionaries
- difference is 287 - 164 = 123

The difference in the number of dictionaries between the two sets is 123.

This 5-mark question was from Singapore Chinese Girls' School 2009 P6 SA1 Maths paper 2 Q17 and the worksheet's answer was 120.Hope to have comments/interpretations from other members in this forum about this dictionaries problem sum on whether the shelves are stacked vertical or placed horizontally side by side etc.

Submitted by VC's mum[/quote]
Hi VC’s mum,

Think the difference in the answers is due to the fact that the assumption made on the type of shelf is not the same. I’ve assumed the shelf to be closed end (conventional type) whereas some others like Mathsguru had assumed the sides are open.

If the sides are closed, then we have 205cm length per shelf. To re-arrange the new dictionaries that are 5mm thick and we are only able to fit in 71 dictionaries per row of shelf. (even if the shelves are placed side by side)

Yes, you are also correct to say that the 4 shelves that are open ended can be joined horizontally to get a long shelf of 820cm length. Here, the 0.75 of dictionary that does not fit into the closed end shelf will fit into this open ended shelf giving space for (0.75 x 4 = 3 additional dictionaries)

Therefore, if shelf is closed ended, we get 120 dictionaries and if it is open ended then 3 additional dictionaries can be squeezed in to get 123 dictionaries.

I guess the question is quite ambiguous and both answers are correct.

[Almighty]

Thankyou very much Sun_2010 for quick reply on my speed problem…

[YLH88]

[quote]
Vanilla Cake wrote :
Hi YLH88,
Thanks for your highlight. You are right and you can take 21+35 which is easier to explain at P6 level. As highlighted by Dharma, pls add the number of pages read by Samir for the first 5 days (5x7=35) and add on the pages read for the next 28 days(28x7=196). So, total pages read by Samir should be 35+196=231 by then (5+28=33 days).

Thanks to Dharma for correcting my workings.[/quote]Hi Vanilla Cake, Dharma,

Sorry, I have 1 more question regarding the question above.
35 is the no of pages Dion has to read to catch but
21 is the no of pages Dion has read ahead of Samir,
why do we take 35 + 21 ?

Sorry, still abit blur on this question :?

[Dharma]

YLH88:

[quote]
Vanilla Cake wrote :
Hi YLH88,
Thanks for your highlight. You are right and you can take 21+35 which is easier to explain at P6 level. As highlighted by Dharma, pls add the number of pages read by Samir for the first 5 days (5x7=35) and add on the pages read for the next 28 days(28x7=196). So, total pages read by Samir should be 35+196=231 by then (5+28=33 days).

Thanks to Dharma for correcting my workings.

Hi Vanilla Cake, Dharma,

Sorry, I have 1 more question regarding the question above.
35 is the no of pages Dion has to read to catch but
21 is the no of pages Dion has read ahead of Samir,
why do we take 35 + 21 ?

Sorry, still abit blur on this question :?[/quote]Hi YLH88,

Here is another approach. See if you can understand.

Let us just try to find out the number of days taken Dion takes to read the same number of pages as Samir.

We try to convert this rate qns to speed qns which we may be more familiar with

When Dion starts to read, Samir had already read 35 pages (5days x 7 pages/day).

No. of days taken by Dion to catch up the no. of pages read by Samir
= 35 pages/ (9pages/day – 7 pages/day)
= 17.5 days

No. of days taken by Dion to read 21 more pages than Samir = 17.5 days + (21days/2 pages/day) = 28 days.

No. of days taken by Samir = 5 days + 28 days = 33 days.
No. of pages read by Samir = 33 days x 7 pages/day = 231 pages

[Almighty]

Hi,


Can anyone help to solve the following problems?

1)Bob and Tina started in opposite directions.Bob drove at 75 Km/h for 4 hours and found that they were 564 km apart.What was the average speed of Tina?
Ans:66Km/h

2)Mr.Lee had 36 more guppies than angelfish.He sold 1/4 of the guppies and 1/5 of the anglefish. He found that he had sold 28 more guppies than anglefish.(Model or algebra method please)
a)How many guppies did Mr.Lee have at first?Ans:416

[CoffeeCat]

Almighty:

Hi,


Can anyone help to solve the following problems?

1)Bob and Tina started in opposite directions.Bob drove at 75 Km/h for 4 hours and found that they were 564 km apart.What was the average speed of Tina?
Ans:66Km/h

2)Mr.Lee had 36 more guppies than angelfish.He sold 1/4 of the guppies and 1/5 of the anglefish. He found that he had sold 28 more guppies than anglefish.(Model or algebra method please)
a)How many guppies did Mr.Lee have at first?Ans:416

The first question is vague but they mean started at the same point but towards different direction. Bob will travel (75*4=300 km) in 4 hours.
thus Tina would have travelled (564-300=264)km in 4 hours.
Therefore tina 's aversge speed will be 264/4 = 66km/h.

For second question. If you are drawing a model, 20 units for angelfish,, 20units + 1 piece sticking out for the 36 more guppies.
When you sold 1/5 of angelfish you sold 4units of angelfish.
When you sold 1/4 of guippies you sold 5 units of guppies and 9 guppies.
Therefore 1 unit of fish = 28-9 = 19.
Guppies at first = (19 * 20 ) + 36 = 416

[YLH88]

Hi Dharma,


Yes, I’m able to understand your explanation. Thank you!!

Hi Vanilla Cake,
Also a big thank you for your help!

Regards

[firebird]

Dear mathsguru


Good morning

Please help me on the following P6 Speed math:

A Van left Port Penang for Town Lalu at 9 a.m. A Car started its journey along the same route as the Van from starting point, two hours later. The car overtook the Van at 3 p.m. The speed of the car was 30 Km/h higher than Van. The Van took 7 hours to reach Town Lalu. Find the distance between Port Penang and Town Lalu.

The answer given was:

a) The speed of the car was 30 km/h more than the speed of the Van.
So 1hr = 30 km
4hr = 4 X 30 = 120 Km

I can understand this. Reason is 4 hours = (11am - 3 pm)


b) Distance travelled from Port Penang to Town Lalu
2 hours = 120 Km
7 hours = 120/2 X 7 = 420 Km (which is the answer given)

I really do not understand how 2 hours is linked to 120 km

Please help me as to how 2 hours is linked to 120 km.
Are there different method/steps / explaination available?

Thank you
Firebird