Secondary Upper and Lower Bound QUESTION

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Discussion Overview

The discussion revolves around a mathematical problem involving upper and lower bounds in the context of determining whether Adrian has enough orange squash to fill 48 glasses. The problem includes aspects of measurement accuracy and requires participants to explore how to apply upper and lower bounds to solve the question.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses frustration with the exam question and outlines their calculations for the upper and lower bounds of the orange squash and glass measurements.
  • Another participant asks for clarification on how to solve the problem, indicating uncertainty about the approach to take.
  • Some participants suggest dividing the upper and lower bounds, but express doubt about whether this method is appropriate for the problem.
  • There is a discussion about the total amount of orange squash needed, with estimates around 12,000ml being proposed by multiple participants.
  • One participant questions why the upper bound is necessary if each glass is stated to hold 250ml, leading to an explanation about the variability in the actual capacity of the glasses.
  • A later reply confirms that the maximum amount needed would be 12,240ml if each glass holds the upper bound of 255ml.

Areas of Agreement / Disagreement

Participants express differing views on the correct method to apply upper and lower bounds, with no consensus reached on the best approach to solve the problem. There is also uncertainty regarding the exact amount of orange squash needed, with estimates varying among participants.

Contextual Notes

Participants rely on their understanding of upper and lower bounds, but there are indications of confusion regarding their application in this specific context. Some assumptions about the measurements and their implications remain unresolved.

Physiona
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I'm pretty frustrated with this exam question:
Adrian is making some orange squash.
He makes 13 litres of orange squash correct to the nearest litre.
Each glass holds 250ml of orange squash correct to the nearest 10ml.
Adrian has 48 glasses.
Does he have enough orange squash to fill all 48 glasses?

I presume this is easy, according to the working out I have done:
Orange Squash
U.B --> 13,500ml (I converted it from Litres to millilitres)
L.B --> 12,500ml

Glass
U.B ---> 245ml
L.B ----> 255ml.
According to the mark scheme, I multiply 48 by the upper bound of the glass; I haven't been taught this way, can someone help?
Thank you.
 
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How would you solve the problem?
 
Well, so far I'd solve it as shown, and then I'd probably divide it, my teacher consulted to us if we require finding the Upper bound of something it would be:
U.B/L.B. But applying that knowledge here, I don't think it's the right way...? As mentioned, I'm not entirely sure how I'd solve it from where I have left off.
 
Physiona said:
Well, so far I'd solve it as shown, and then I'd probably divide it, my teacher consulted to us if we require finding the Upper bound of something it would be:
U.B/L.B. But applying that knowledge here, I don't think it's the right way...? As mentioned, I'm not entirely sure how I'd solve it from where I have left off.

How much squash do you think you might need (at most)?
 
I think you'd need roughly 12,000 (ish) ml of orange squash. He's made 13,000ml all together, and he has 48 cups. I don't think he can exceed the limit of 13,000ml if I'm right... Not exactly sure.
 
Physiona said:
I think you'd need roughly 12,000 (ish) ml of orange squash. He's made 13,000ml all together, and he has 48 cups. I don't think he can exceed the limit of 13,000ml if I'm right... Not exactly sure.

I didn't ask how much he made. I asked how much he might need. Hint: he needs to fill 48 glasses.
 
Wouldn't he need the same amount though, of approx. 12,000ml?
 
wait, would he need, 12240ml?
 
Physiona said:
wait, would he need, 12240ml?

Yes, that's most he could possibly need: if every glass is ##255ml##.
 
  • #10
But isn't each glass 250ml, why do we require to use the U.B?
 
  • #11
Physiona said:
But isn't each glass 250ml, why do we require to use the U.B?

Because you don't know exactly how much each glass holds. It might hold only ##245ml## and it might hold as much as ##255ml##.
 
  • #12
Aha, that makes so much sense now.
Thank you so much!
 

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