Help with Maths ratio problem?

My nephew has been sent a maths ratio problem. Would be great if you could show the method to working it out for me to explain to him.

Paul wants to make a fizzy drink. His recipe says it needs:-

5 parts lime juice

3 parts lemonade

He thinks he has 300ml of Lime juice and 200ml of lemonade.

if that’s right then what is the maximum amount of fizzy drink he can make from this?

thanks

One of the supplied ingredients will have a left over. 300mL of lime being 5 parts means one part is 60mL (300/5). To make up the fiz to the recipe would therefore need 3* 60 = 180 mL of lemonade, so the lemonade is in excess, and he can make 300 + 180 = 480 mL of fiz.

In these straitened times in reality I'd just bung in all the lemonade, don't waste it!

480 ml with 20 ml of lemonade left over.

The simple intuitive method of calculation:

Every 8ml of product require 5ml of lime and 3ml of lemonade

300ml lime would make 300/5 lots of 8ml = 60

200ml of lemonade would make 200/3 lot of 8ml = 66 2/3 lots of 8ml

Clearly there is insufficient lime to make 66 2/3 lots of 8ml, so the answer is 60 lots of 8ml = 480ml

Materials totalled 500ml, so 500ml-480ml = 20ml (of lemonade) left over.

In reality, just mix the whole lot together and the error in ratios is not that great🙂. Not many would notice the difference!

Thanks that makes sense

Paul should have said "to hell with lemonade where's the soothing real ale?"

Correct answer:

Use the lime to put in your Corona/Sol and give the lemonade to the kids.

I'm thirsty...

Strictly speaking he can make 500ml of fizzy drink. 480ml of lime/lemonade mix and 20ml of straight lemonade.

That is why exam questions have to be worded very carefully🙂 - to avoid the smart ar posteriors! Like the classic of finding x for a right angled triangle with the values given for two sides of the triangle and the bright spark who puts a ring around the x on the diagram and writes “here it is”.

It’s not only GCSE that make bloomers. I came across one where one was expected to provide the power of a wind turbine if the rotor diameter was doubled. The ‘naughty’ answer might be ‘No change - or the magic smoke would be let out!’.

Top marks.

 Another defining attribute is he THINKS he has . ????

Steve.

Edited By Steviegtr on 15/04/2020 23:30:20

Actually as it's cooking not maths the right answer is use it all, it's close enough for my kitchen!

Nah. It takes 50 years to turn school students imbued with the required native common sense into pedantic nitpickers with the spare time to sit around and split such hairs. (And mix such metaphors!).

Thanks that makes sense

The advent of precise single pan weighing devices has complicated cooking recipes to an extent. In the days of old the other ingredients would likely be balanced against the number of eggs on the other pan. Simple ratios, so the cake, or whatever, came out sized according to small or large eggs, not precise weights of every ingredient. Such is progress🙂.

There were never any ‘part eggs’ left over and the product would be just as consistent from one session to another - apart from the slightly different size - as those made by more modern equipment.

On the plus side for these days, all the ingredients can be added to the mixing bowl, tared on the weighing device so people who can not do maths can at least simply follow the weights quoted in the recipe.

(1) A method I haven't seen mentioned is linear programming (nothing to do with computers) where you find the answer with a bit of graph paper where the x axis equals one variable and the y axis represents the other. Take a look at Wikipedia for a more detailed explanation. Wikipedia

(2) If you want to work out the optimal ratios for more than two variables you would move onto the simplex method. Again, an explanation from Wikipedia here. Wikipedia

(3) For a few extra brownie points you can also use the SOLVER add-in in Excel. Its not part of the standard installation so you need to go to Files>Options>Add-ins to activate it. (The underlying method is simplex)

There you are guys, be careful of asking questions like this when there are ex-accountants lurking around.

There you are guys, be careful of asking questions like this when there are ex-accountants lurking around.

That is half the trouble with accountants. They would look to save that 20ml of lemonade for another day!

And it would likely actually cost more, in time and resources, to measure out that 180ml than pouring in the full 200!🙂

So many imporant factors left out of the question. What brand of lemonade? Sugar free? Sweetener type? Is the lime juice fresh squeezed or a sweetened cordial? Personally I'd run a taste test first 'cos i hate things too sweet.

Don't forget the warning label about obesity and tooth damage

Remember that old exam question for kiddies; Which is the odd one out of a banana, a lemon and an orange?

2 are citrus, 2 are yellow, 2 are sweet.

It gets even more involved if we stop assuming it's ripe common fruit being refered to. Banana is a monocot whereas citrus are dicotyledonous and even more involved when discussing bitter oranges and sweet lemons. and the whole plantain family. Apple bananas anyone? Musa bananas v Ensete bananas?

(I had and was a lot of trouble at school)

pgk

Which is the odd one out of 'banana, lemon, and orange'? [edited so it works better...]

The answere is, of course, 'and'. (Thanks to the film 'Funny Bones' for that...)

Seriously, what age of pupil was this question aimed at? And what is the typical age of this thread's participants? No wonder thread-cutting gear train problems still keep coming up...

However, the OP asks a valid question about explanation of the method; he's not asking what the answer is. Having tried to teach/explain a few mathematically-based things to graduates - and failed abysmally - I have great respect for good maths teachers. Unfortunately, they seem to be few and far between. I was lucky, but, of course, didn't know it at the time.

Edited By Kiwi Bloke on 16/04/2020 08:36:47

One that is probably apocryphal 'Take 3 from one hundred as many times as you can. What are you left with?'

'I have taken 3 from 100 loads of times and I am always left with 97'

And one that is true as I saw it myself on an ICT exam paper - 'What is backup?'

'It is when the police are at an incident and they call for more help'

Absolutely true!

That was an entrance exam question for prep school. I'd guess I was about 9 or 10yrs old The only question that threw me was 'What are baby rabbits called'

I knew baby hares were leverets but i'd not heard the term kittens for young rabbits back then and it haunted me for years...

I ws probably a little sh!t back then. At least I've got bigger.....

pgk