Melody

The area of the small one is certainly 9/16 of the big one but I do not think that this is what the question is asking ...

At least that is not how i interpreted it.

I interpreted it as the intersection of the  areas divided by the original big area.  This is a harder question.

Hi Builderboi,

Thanks for all your great answers.

I do have a suggestion though.

Try experimenting with giving answers that encourage askers to learn and that make it more difficult for them to just copy.

Like here you could have said.

"Try adding all the left sides and putting the answer equal to the sum of all the right sides.  See what you get ;)"

People are much more likely to learn from you if you do not do all the work for them.

Teaching is a learned art.  

Are there meant to be pics with this?

Next time try a heading like.

"Repost.... I'd still really appreciate an answer"

Answered on original.

Please no one answer over me.

Let the amount that is left in the big one be x  AFTER  the amount has been tipped into the cup.

Which means that 1/6 of x is tipped into the cup

which means that originally there was 7/6 of x in the jug.

So the cup now has x/6  ml in it If we add 50ml that will be     x/6+50 millilitres    

and we are told htat that will be 1/5 of what is now in the pitcher  (how much was that again)

Draw a pic to help you see what is happening.

Set up a simple equation, solve for x, then solve for the amount of water that was in the pitcher in the first place.

You should do, or at least seriously try,  the others for yourself.

Let's see

I'm going to look at c

\(f(x)=\lfloor x\lfloor x\rfloor \rfloor=5 \qquad \text{find all }x\ge 0\\ \lfloor x\lfloor x\rfloor \rfloor=5\\ 5\le x\lfloor x\rfloor <6\\ 5\le x\lfloor x\rfloor <6\\ let \;\;x=k+\delta\qquad \text{where k is an integer }k\ge0 \text{ and }0\le\delta<1\\ 5\le k(k+\delta )<6\\ x=k+\delta = 2.5\;\;works,\\ \text{ in fact x can equal any number from 2.5 up to and not including 3}\\ 2.5\le x <3 \)

LaTex:

f(x)=\lfloor x\lfloor x\rfloor \rfloor=5 \qquad \text{find all }x\ge 0\\
\lfloor x\lfloor x\rfloor \rfloor=5\\
5\le x\lfloor x\rfloor <6\\
5\le x\lfloor x\rfloor <6\\
let \;\;x=k+\delta\qquad \text{where k is an integer  }k\ge0    \text{ and  }0\le\delta<1\\
5\le k(k+\delta )<6\\
x=k+\delta = 2.5\;\;works,\\
\text{ in fact x can equal any number from 2.5 up to and not including 3}\\
2.5\le x <3

Firstly you need to work out how many prime factors there are between 30 and 140

You can do that with a seive of Eratosthense.

What are the numbers? Do you want us to list them? All 10 to 20 thousand of them?