Q&A - P3 Math

[Dharma]

fanren:

BigDevil:

[quote=\"fanren\"]Hi

i have a qn hope someone can help.

Bobby places 12 cards on a table. Each card is either red or black in colour. If the fraction of black cards is 7/12, what is the smallest number of additionals cards that Bobby needs to put on the table so that the fraction of black cards becomes 5/8 ?

thanks in advance!

Not sure if my understanding is correct...

7/12 = 14/24
5/8 = 15/24

So Bobby needs to put 1 additional card?

the answer is 4 cards, i am thinking is it 5/8 = 10/16, so 12 + 4 = 16 ? hope someone who knows can help and share. thanks

thanks BigDevil for trying ![/quote]Hope this helps

At first
Black : 7
Red : 5

If B number of black cars added and R number of red cards added

Black : 7 + B
Red : 5 + R
Total no. of cards = 12 + B + R

Fraction of black cards = 7 + B/ (12 + B + R) = 5/8
Fraction of red cards = 5 + R/ (12 + B + R) = 3/8

8(7+B) = 5(12 + B + R)
56 + 8B = 60 + 5B + 5R
3B = 5R + 4

Smallest no. of cards added is by adding 1 red card ; and 3 black cards
3B = 5(1) + 4
B = 9/3 = 3
B + R = 3 + 1 = 4

New fraction of black cards = 7 + 3/ (12 + 3 + 1) = 10/16 = 5/8

[BigDevil]

:faint:

[fanren]

Thanks a million for your answer plus explanation, Dharma!!!

[P5G]

fanren:

Hi

i have a qn hope someone can help.

Bobby places 12 cards on a table. Each card is either red or black in colour. If the fraction of black cards is 7/12, what is the smallest number of additional cards that Bobby needs to put on the table so that the fraction of black cards becomes 5/8 ?

thanks in advance!

Sorry for the blunder. Below are my corrections.

5/8 x 2/2 = 10/16

16 - 12 = 4 additional cards

[Herbie]

Mrs Lim bought a few chicken pies and apple pies for $38. Each apple pie cost $0.60 and each chicken pie cost 2/3 more than an apple pie. 3/5 of what she bought was apple pie, how many chicken pie did she buy?


Can someone help to solve this qn? Tx

[CoffeeCat]

Herbie:

Mrs Lim bought a few chicken pies and apple pies for $38. Each apple pie cost $0.60 and each chicken pie cost 2/3 more than an apple pie. 3/5 of what she bought was apple pie, how many chicken pie did she buy?


Can someone help to solve this qn? Tx

First find cost of chicken pie = (3+2)/3 times $0.60 = $1.00
3/5 are apple pie, 2/5 are chicken pie, meaning for every 3 apple pies there are 2 chicken pies, so we group this 5 pies together and their cost will be
($0.60 * 3) + ($1.00 * 2) = $3.80

To find number of such groups, divide $38 by $3.80 = 10.
Therefore there are (10 * 2 = 20) chicken pies

[Herbie]

Thanks CoffeeCat,


I have another maths qn. Can help to solve it? Tx

Mr Tan had 1.5 litres of white paint on Tin A and 1.25litres of blue paint in Tin B. He poured 750ml of blue paint from TIn B into Tin A. He then poured some of the mixture in Tin A back into Tin B. if 7/11 of the final mixture in Tin B was made up of blue paint, what does the volume of mixture in Tin A that Mr Tan had poured into Tin B?

[CoffeeCat]

Herbie:

Thanks CoffeeCat,


I have another maths qn. Can help to solve it? Tx

Mr Tan had 1.5 litres of white paint on Tin A and 1.25litres of blue paint in Tin B. He poured 750ml of blue paint from TIn B into Tin A. He then poured some of the mixture in Tin A back into Tin B. if 7/11 of the final mixture in Tin B was made up of blue paint, what does the volume of mixture in Tin A that Mr Tan had poured into Tin B?

Hmm may i ask where you get these qns from? This kinda question used to be challenging and appear in math competition.
The key to solving is to note the ratio of blue to white paint in A after the first transfer.
750 : 1500 = 1: 2.
if 4/11 of the final mixture is white paint, then 2/11 of the final mixture must be the blue paint from A. therefore 5 /11 of final mixture = 0.5 litres. From this you find 6/11 of final mixtures = 0.6litres

[Herbie]

Hi CoffeeCat,


I can’t see how the ratio of 1: 2 is used to solve the problem. Also how you get the 2/11? Can explain in more detail?

Many thanks!

[CoffeeCat]

Herbie:

Hi CoffeeCat,


I can't see how the ratio of 1: 2 is used to solve the problem. Also how you get the 2/11? Can explain in more detail?

Many thanks!

oh because in such \"transfer here transfer there\" question, after the first transfer, it is always assumed thatt he impure mixture will be evenly mixed, thus the ratio is important. Because later when you transfer the impure mixture back, you are transferring a mixture with that ratio of constituents.
In the new mixture in A, you have 2 litres of whitepaint for every 1 litre of blue paint.