Chapter 5.2, Problem 26P

Tell whether the two quantities vary directly. Explain your reasoning.

A recipe that calls for 2 cups of sugar for each cup of flour

To determine

To Explain: Whether the two quantities vary directly or not for sugar and flour.

Answer to Problem 26P

Yes! The two quantities vary directly. Sugar increase directly with cup of flour. Because ratio of sugar and flour are constant to make a recipe.

Explanation of Solution

Given information: A recipe that calls for 2 cups of sugar for each cup of flour.

From given information if recipe uses 1 cup of flour it needs 2 cups of sugar.

Ratio of sugar to flour is $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$1$}\right.=2$ .

The ratio of flour to sugar will be constant to make that recipe regardless of the quantity that need to make.

That’s 2 cups of flour needs 4 cups of sugar. The sugar need is double the amount of flour used.

Ratio of sugar to flour is $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=2$ .

Hence the sugar to flour ratio is constant. So, it is direct variation.