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November 01, 2025, 10:02:23 am
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Author Topic: Number patterns problem  (Read 1148 times)  Share 

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onur369

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Number patterns problem
« on: May 30, 2011, 08:48:53 pm »
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Just did my sac today and this was one of the questions:

Question 1
On the O’Callaghans’ farm there is only 10 000 litres of water left in their tank. They need to buy more water which is delivered by a water tanker. The water is pumped from the water tanker into the tank at a constant rate of 800 litres per minute.

If tn litres denotes the amount of water in the tank n minutes after pumping starts, we can write
tn = a + bn.
Determine the values of a and b.

In the answer sheet it says a is 10000 and b is 800. But I did a=9200 and b is 800 how?

Simply by implying the tn=a + (n-1)x d
tn=10000+(n-1)x800
tn=10000+800n-800
tn=9200+800n

? DO I HAVE A POINT?
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acrimony

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Re: Number patterns problem
« Reply #1 on: May 30, 2011, 08:54:39 pm »
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a= 9200 is the answer, there can be no other answer
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onur369

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Re: Number patterns problem
« Reply #2 on: May 30, 2011, 08:56:34 pm »
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Well VCAA says 10000.
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acrimony

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Re: Number patterns problem
« Reply #3 on: May 30, 2011, 09:03:12 pm »
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Please link me, what exam was it?
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onur369

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Re: Number patterns problem
« Reply #4 on: May 30, 2011, 09:07:22 pm »
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VCAA 2003, but I beleive both answers will be correct. Mathematically Im correct.
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acrimony

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Re: Number patterns problem
« Reply #5 on: May 30, 2011, 09:08:48 pm »
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Quote from: onur369 on May 30, 2011, 09:07:22 pm
VCAA 2003, but I beleive both answers will be correct. Mathematically Im correct.

I cannot comprehend how the answer is 10000
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sam.utute

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Re: Number patterns problem
« Reply #6 on: May 30, 2011, 09:13:18 pm »
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Using your answer:

t(n) = 9200 + 800n

Logically, the tank will contain 10800L after 1 minute, right?
If we sub in 1, into your equation...

t(1) = 9200 + 800 x 1 = 10000 ≠ 10800

The trick to number patterns is to work out what "n" denotes. In this case, it means the number of L in the tank after that many minutes. So, a has to equal 10000, because at 0 minutes, there should be 10000L in the tank.
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onur369

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Re: Number patterns problem
« Reply #7 on: May 30, 2011, 09:20:32 pm »
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Ok but then again its in the form the question wants it and I used an arithmetic rule, it shouldnt be wrong in my opinion. We will just have to see.
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sam.utute

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Re: Number patterns problem
« Reply #8 on: May 30, 2011, 10:03:03 pm »
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You used the correct forumla, but were basing it on an incorrect assumption.

You should have used "n", not (n-1). The reason being that the tank is filled after n minutes.

So the equation should change to:
t(n) = a + n x d

Hard to explain, but important nonetheless.
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Kaza8694

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Re: Number patterns problem
« Reply #9 on: June 20, 2011, 11:13:49 pm »
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The tank already has 10000 litres.  This is the amount of water at t(0).  Confirm by t(0)=10000+ 0x800=10000.

Your answer is wrong because it gives an answer at t(0) the tank has 9200 litres.
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Keo

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Re: Number patterns problem
« Reply #10 on: June 21, 2011, 05:47:27 pm »
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a = first term
hence a, will be 10,000 as this is your initial term you started off with
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