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By: Strawberry (offline)  Thursday, September 11 2014 @ 02:02 AM CDT (Read 1517 times)  
Strawberry

Q1 Tap A fills a container in 3 hours. Tap B fills the same container in 2 hours. Tap C empties the same container in 6 hours. When all the taps are turned on at the same time, how long does it take to fill the container.

Q2 Anna baked some chicken and beef pies for her friends. 45% of the chicken pies and 10% of the beef pies were eaten. Altogether, 1/3 of the pies were eaten. In the end, she was left with 10 more chicken pies than beef pies. How many chicken pies did she bake?

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By: jo sarah (offline)  Thursday, September 11 2014 @ 02:33 AM CDT  
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Hi, here are solutions, and hope they are useful.

Q1 Tap A fills a container in 3 hours. Tap B fills the same container in 2 hours. Tap C empties the same container in 6 hours. When all the taps are turned on at the same time, how long does it take to fill the container.

Solution:
You work this by using a standardised 1 hour for all taps:

so in 1 hour, Tap A fills 1/3, B fills 1/2 and C empties 1/6 of container.

Thus, in 1 hour, all three together fill (1/3 + 1/2 - 1/6) = 4/6 = 2/3 of container.

Therefore, to fill container, it'll take 3/2 = 1.5 hours.


Q2 Anna baked some chicken and beef pies for her friends. 45% of the chicken pies and 10% of the beef pies were eaten. Altogether, 1/3 of the pies were eaten. In the end, she was left with 10 more chicken pies than beef pies. How many chicken pies did she bake?

Solution:
If you let her bake 100 units (u) of chicken pie, and 100 parts (p) of beef pies.

Pies eaten: 45u chicken, and 10p beef

so that, 45u + 10p = (100u + 100p) / 3...................because what's eaten constitutes 1/3 of all pies.

that is, 45u + 10p = (100/3)u + (100/3)p

So, 35 u = 70p

i.e., 1 u = 2 p


Now, she's left with 55u chicken and 90p beef.

which difference is: 55u - 90p = 110p - 90p = 20p ..............[edited, to correct typo which affect following steps; now corrected]

Thus, 20p --> 10 pies

therefore, 1p --> 1/2 pie

so that she baked 100u = 200p = 100 chicken pies


Hope this is helpful Smile

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By: echeewh (offline)  Thursday, September 11 2014 @ 07:08 AM CDT  
echeewh

Hey <Strawberry>,

Noted there was a mistake made in <jo sarah>'s solution to Q2. Error is shown in bold red.

Following is the <Correction>:

Now, she's left with 55u chicken and 90p beef.

which difference is: 55u - 90p = 110p - 90p = 20p

Thus, 20p --> 10 pies

therefore, 1p --> (1/2) pie

so that she baked 100u = 200p = 100 chicken pies

=======

Trust this helps.

Cheers,
Edward

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By: Strawberry (offline)  Thursday, September 11 2014 @ 08:48 AM CDT  
Strawberry

Thank you both...

a quick question for Q2, how to we know it is 100 u and 100 p and not other amount..

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By: jo sarah (offline)  Thursday, September 11 2014 @ 09:01 AM CDT  
jo sarah

Hi,

Sorry, it's a careless error, and I trust you can follow the reasoning in the solution Smile. and that's crucial. If you can, you'll be able to handle any other similar questions.

Note I say "if you let her bake..."
I have used 100u and 100p, because
A. There are two unknown quantities so you need to use two names -- parts and units. In algebra, we may use two letters, say, c and b.
B. I used 100u and 100p out of convenience, because the question speaks of percentages, even 45% which is not so easy to convert to a convenient fraction. The thinking is quite like if the question speaks of two fractions, say, 1/3 and 1/2, and you start using 6 units, choosing a no. that divides 2 and 3 exactly. We may simply start with 1u and 1p respectively. In that case you will need to handle fractions or decimals. For those with no problems with fractions or decimals, I usually go ahead using them.

Hope this explains. Smile

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By: Strawberry (offline)  Thursday, September 11 2014 @ 08:43 PM CDT  
Strawberry

Thank you... it very well-explained =)

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