Question

Susan mixes red and blue paint to make purple.

Red
2 parts of red paint with 3 parts of blue paint make purple.
Susan has 50 ml of red and 100 ml of blue.
What is the maximum amount of purple she can make?

Answer 1

125 mL

Explanation:

Susan's purple paint has the proportions 2 parts red and 3 parts blue. That means the total amount of paint is (2+3)/2 = 5/2 the amount of red paint, or (2+3)/3 = 5/3 the amount of blue paint.

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The total amount of paint Susan has is 50 mL +100 mL = 150 mL.

If Susan uses all of her red paint (with sufficient blue paint), she would have an amount of purple paint equal to ...

(5/2)(50 mL) = 125 mL . . . . purple paint

If Susan uses all of her blue paint (with sufficient red paint), she would have an amount of purple paint equal to ...

(5/3)(100 mL) = 166 2/3 mL . . . . purple paint

This is more paint than Susan has, so the amount of purple paint Susan can make is limited by the amount of red paint she has. Susan can make a maximum of 125 mL of purple paint.

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Additional comment

Essentially, we have rewritten the proportion to show corresponding amounts of red and blue paint:

red : blue = 2 : 3 = 50 : 75 = 66 2/3 : 100

Since Susan has only 50 mL of red, and more than 75 mL of blue, the red paint is the limiting ingredient.