Stretch Your Thinking

Question

The directions for lemonade say to put 2 cups of the liquid concentrate into 1 gallon of water. If Olivia only wants to make 1 pint of lemonade, how many fluid ounces of concentrate should she use? Explain.

Answer 1

This problem is a proportion, namely 2 cups : 1 gallon :: x cups : 1 pint

 

We know that 1 cup = 8 ounces, 1 pint = 16 ounces, and 1 gallon = 128 ounces, and 2 cups = 16 punces

 

So, 16 ounces / 128 ounces = x ounces / 16 ounces

 

When we cross multiply, we get 16o • 16 o = x • 128 o

 

Solving, x = 256 o² / 128 o = 2 ounces

Answer 2

For this problem, you need to know the number of pints that are in a gallon.  

Since there are 8 pints in a gallon, Olivia would want to use 1/8 of the 2 cups of liquid concentrate

This can be shown by 2 cups * .125 (which is 1/8) = 1/4

 

You must also know that there are 16 ounces in 2 cups

The number of ounces of concentrate needed can be shown by taking 16 ounces * .25, or 1/8

 

Olivia would need .25 of a cup which equals 1/4 cup or 2 ounces of concentrate to make the lemonade.