Tutor MathsGuru: Ask me for your burning Maths questions!

[adhdadhd]

Vanilla Cake:

A has 200 more books than B. A gives 60% of her books to B. B then gives 25% of her books back to A. In the end, B has 200 more books than A. How many books does A have at first?

A has 200 more than B
A [4u | 4u | 4u | 4u | 4u] [200]
B [4u | 4u | 4u | 4u | 4u]

A gives 60% to B, ie: gives away 12u + 120
A [4u | 4u] [80]
B [4u | 4u | 4u | 4u | 4u| 4u | 4u | 4u] [120]

B gives 25% to A, ie: 32u/4 + 120/4 = 8u + 30
A [4u | 4u | 4u | 4u ] [110]
B [4u | 4u | 4u | 4u | 4u | 4u] [90]

In the end, B has 200 more than A
A [4u | 4u | 4u | 4u ] [110]|<200>|
B [4u | 4u | 4u | 4u | 4u | 4u] [90]
OR,
A [4u | 4u | 4u | 4u ] [110][110][90]
B [4u | 4u | 4u | 4u ] [ 4u | 4u ][90]

As you can see, 110 + 200 = 8u + 90, so 8u= 310-90 = 220,
thus 1 u = 27.5

'A' has 20u +200 = 750 books, at first.

[david59]

Jolyn:

Guan Hui:

hi jolyn,


1)
when you transfer 30 books from box to shelf.
box will minus 30 books while shelf increase 30 books.
originally there were 84 more books on the shelf than box.
so... 84 +30+30=144 more books on shelf than in box now.

2)
514 face towels 312 hand towels
total = 514+312=826 towels
Total towels sold =1982
Number of bath towel=1982-826=1156
how many more? 1156-514=642 towels more

Hi Guan Hui

Thanks for your answer but I do not understand as follows:

1. Why it is 84+30+30 and not 84+30-30? As box minus 30 and shelf increase 30....

Thks
Jolyn

The reason is easier to see in the model method.

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

[Maths Monster]

delete

[Maths Monster]

delete

[wkong]

Dear MathsGuru,


Can you pls help for the following question and provide me the method?


A container 5/6 full of sand has a mass of 108kg. The same container ¼ full of sugar has a mass of 30kg. The container when full of sand is 60kg heavier than when it is full of sugar. Find the mass of the empty container.

Thanks.

[small]

Vanilla Cake:

Plus this one from http://www.orlesson.org/orp/09Ma/2009-Math-SA1-TaoNan.pdf.


Leela and Kumar shared a sum of money. Leela's share was $90 less than Kumar's. After Kumar gave 1/7 of his share to Leela, Leela had $10 more than Kumar.

(a) How much did Leela have at first?
(b) What was the sum of money?

Cannot understand the given solution in the link, :stupid: Pls help with model solution.
TIA for all your help.

This is my solution for your second question.

http://www.postimage.org/image.php?v=Tsd7RS9

[CoffeeCat]

wkong:

Dear MathsGuru,


Can you pls help for the following question and provide me the method?


A container 5/6 full of sand has a mass of 108kg. The same container ¼ full of sugar has a mass of 30kg. The container when full of sand is 60kg heavier than when it is full of sugar. Find the mass of the empty container.

Thanks.

Given
Weight of container + 5/6 sand = 108kg --- (1)
Weight of container + 1/4 sugar = 30kg --- (2)

Weight of container + 6/6 sand = Weight of container + 4/4 sugar + 60kg
==> 6/6 sand = 4/4 sugar + 60kg --- (3)

Multiplying (1) by 6 [to get rid of the fractional denominator]
Weight of 6 containers + 5 sand = 108kg * 6 = 648kg --- (4)

Multiplying (2) by 4 [to get rid of the fractional denominator]
Weight of 4 containers + 1 sugar = 120 kg --- (5)

Using (3)...
Weight of 4 containers + 1sugar + 60 kg =
Weight of 4 containers + 1 sand = 120 + 60 = 180 kg

Weight of 20 containers + 5 sand = 180 * 5 = 900 kg
Weight of 14 containers = 900kg - 648 kg = 252kg
Weight of 1 (empty) container = 252/14 = 18kg

[trytry]

wkong:

Dear MathsGuru,


Can you pls help for the following question and provide me the method?


A container 5/6 full of sand has a mass of 108kg. The same container ¼ full of sugar has a mass of 30kg. The container when full of sand is 60kg heavier than when it is full of sugar. Find the mass of the empty container.

Thanks.

........................{.......5/6...........}
sand :container [...][...][...][...][...] 108kg
.........................{1/4}
sugar :container [......][......][......][.....] 30kg


capacity of container same:
........................{.............10/12........}
sand :container [2u][2u ][2u][2u][2u][2u..] 108kg

.........................{3/12}
sugar :container [.3p..][..3p...][..3p..][..3p.] 30kg


Since mass of sand is 60 heavier than mass of sugar when full
===> 12u=12p+60
===> 1u=1p+5

sand: container + 10u= 108kg
sand: container + 10p + 50= 108kg

sugar: container + 3p= 30kg


therefore 7p= 108-30-50 = 28 kg
.....................1p=4kg
.....................3p=12kg
container=30kg-12kg=18kg
try mine best

[Jolyn]

Maths Monster:

Jolyn:

[quote=\"Guan Hui\"]hi jolyn,


1)
when you transfer 30 books from box to shelf.
box will minus 30 books while shelf increase 30 books.
originally there were 84 more books on the shelf than box.
so... 84 +30+30=144 more books on shelf than in box now.

2)
514 face towels 312 hand towels
total = 514+312=826 towels
Total towels sold =1982
Number of bath towel=1982-826=1156
how many more? 1156-514=642 towels more

Hi Guan Hui

Thanks for your answer but I do not understand as follows:

1. Why it is 84+30+30 and not 84+30-30? As box minus 30 and shelf increase 30....

Thks
Jolyn

Hope this model helps:


http://www.postimage.org/image.php?v=aVDVHPr[/quote]Thks for the explained model.

[Jolyn]

david59:

Jolyn:

[quote=\"Guan Hui\"]hi jolyn,


1)
when you transfer 30 books from box to shelf.
box will minus 30 books while shelf increase 30 books.
originally there were 84 more books on the shelf than box.
so... 84 +30+30=144 more books on shelf than in box now.

2)
514 face towels 312 hand towels
total = 514+312=826 towels
Total towels sold =1982
Number of bath towel=1982-826=1156
how many more? 1156-514=642 towels more

Hi Guan Hui

Thanks for your answer but I do not understand as follows:

1. Why it is 84+30+30 and not 84+30-30? As box minus 30 and shelf increase 30....

Thks
Jolyn

The reason is easier to see in the model method.

http://www.postimage.org/image.php?v=gxlAgyS[/quote]It is easier to see in your model method.

Thks....