You may also like

problem icon

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?

problem icon

Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

problem icon


Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Mixing Lemonade

Age 11 to 14 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.

Mixing Lemonade
Click the New Mixes button to generate new mixtures

Beaker A

Lemon ???
Water ???
Beaker B

Lemon ???
Water ???
Which beaker has the stronger tasting lemonade?

Score: 0

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?