Bianca Case Study - Science and Maths Assignment Help

Assignment Task:

1. Playing with numbers.

Bianca is looking after a sick relative and must measure exactly 2mL of medicine. After a long search Bianca only finds two measuring cups, one holds 24mL and the other 35mL. No other measurements are shown on the cups. In fact, these two cups and the medicine bottle are the only containers that the medicine can be put into. And you can't mark the cups in any way. But, most importantly, you can't just judge how much is or is not in a cup, you have to be exact with your measurement of the medicine. 

(a) Using just these two cups (and the medicine bottle) how can Bianca measure 1, 2 or 3mL? Here you should play around with the cups and measurements, stopping when you get to one of those amounts. As you'll see in the example below, carefully explaining what you have done is tricky but important. 

(b) Can Bianca use these to measure exactly 2mL? If you have already answered this, then use these cups to measure exactly 3mL. 

(c) Can Bianca use these two measuring cups to measure lmL? Again, you might have the answer already. If you have, then fill in the gap by making sure you can find all of 1, 2 and 3mL. 

(d) Extension question: Describe a way of getting any possible measurement using these two cups? Or explain why some measures are impossible to get. 

The answers here can be quite complicated. For example, if Bianca only had cups holding 3mL and 7mL then one solution for getting 2mL is 

(i) Fill the 7mL cup 
(ii) Fill the 3mL cup from the full 7mL cup leaving 4mL in that cup 
(iii) Empty the 3mL cup back into the medicine bottle 
(iv) Fill the 3mL cup from the 7mL cup leaving lmL [for part (a) you would stop here] 
(v) Empty the 3mL cup back into the medicine bottle 
(vi) Pour the lime into the 3mL cup leaving the 7mL cup empty 
(vii) Fill the 7mL cup again 
(viii) The 3mL cup has me in it at the moment, now fill that cup with 2mL from the full 7mL cup leaving the big cup holding 5mL 
(ix) Empty the 3mL cup back into the medicine bottle 
(x) Fill the 3mL cup from the full 7mL cup leaving 2mL in the big cup 

You now have your 2mL. You should try playing around with smaller numbers first, then try to solve this problem with your given cup sizes. Cups with sizes 3 and 7 have been used here, you might play with those, or something like 4 and 9, or whatever pair takes your fancy. 
Note: You have to find the exact amount in one go. You can't, work out how to obtain me, and then just repeat that 3 times to say you've got 3mL. You have to end up with exactly 1, 2 or 3mL in one of the cups at the end. 

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