### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### F'arc'tion

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

### Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening? # Mixing Lemonade ##### Stage: 3 Challenge Level: I mixed up some lemonade in two glasses. The first glass had$200$ml of lemon juice and$300$ml of water. The second glass had$100$ml of lemon juice and$200\$ml of water.

Which mixture has the stronger tasting lemonade?
How do you know?

Use the interactivity below to compare different mixtures of lemonade and develop a strategy for deciding which is stronger each time.

Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Once you are confident that you can always work out which mixture is stronger, here are some questions to consider:

How might you use fractions to help you to work out which mixture is stronger?
How might you use ratios?
How about a graphical approach?

Do you always use the same strategy?
Describe some occasions when one strategy might be more efficient than another.

In the original example, the first glass had 200ml of lemon juice and 300ml of water, and the second glass had 100ml of lemon juice and 200ml of water. If I mix the two glasses of lemonade together, the mixture is weaker than the first glass was, but stronger than the second glass.
Try the same with some other mixtures. Is the strength of the combined mixture always between the strengths of the originals? Can you justify your findings?