High School Secondary Upper and Lower Bound QUESTION

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The discussion revolves around calculating whether Adrian has sufficient orange squash to fill 48 glasses, given that he prepares 13 liters of squash, which translates to an upper bound of 13,500ml and a lower bound of 12,500ml. Each glass holds 250ml, with an upper bound of 255ml and a lower bound of 245ml. To determine if he has enough squash, participants clarify that the upper bound of the glass volume must be used for accurate calculations, leading to the conclusion that Adrian needs a maximum of 12,240ml to fill all glasses. Thus, he has enough squash to meet this requirement.

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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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