Mixing Lemonade
We have prepared two pitchers of lemonade for a birthday.
As each one contains different amounts of lemon and water, their lemon flavor is not the same. Which has a stronger flavor?
Reflect
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?
If we combine the two jars into one, how will its lemon flavor be compared to the other two? (major, minor, between the other two, ...)
Try to relate it to this property of fractions:
❝If we have two fractions and we add their numerators on the one hand and their denominators on the other, the value of the fraction obtained is between the two of them❞
Activity based on: Mixing Lemonade https://nrich.maths.org/6870]