Chapter 7.1, Problem 7P

Allie, Benton, and Cathy are planning to mix red and yellow paint. They are considering which of the two following paint mixtures will make a more yellow paint:

• a mixture of 3 cups red and 5 cups yellow

• a mixture of 4 cups red and 6 cups yellow

Allie says that both paints will look the same because to make the second mixture you just add 1 cup of each color to the first mixture. Benton says that the second mixture should be more yellow than the first because it uses more yellow than the first mixture. Cathy says that both paints should look the same because each uses 2 cups more yellow than red.

a. Discuss the students’ ideas. Is their reasoning valid or not?

b. Which paint will be more yellow, and why? Use a ratio table to solve this problem in two different ways, explaining in detail why you can solve the problem the way you do.