Question

The amount y (in cups) of flour is proportional to the number x of eggs in a recipe. The recipe calls for 6 cups of flour for every 4 eggs.

A. Write an equation that represents the situation.
B. How many eggs are included when the recipe uses 12 cups of flour?

Answer 1

To find the number of eggs needed for 12 cups of flour in a recipe where the amount of flour is proportional to the number of eggs (6 cups for every 4 eggs), set up a proportion y/x = 6/4, simplify to y/x = 3/2, solve for x with 12/x = 3/2, cross-multiply and simplify to get x = 8 eggs.

Step-by-step explanation:

The amount of flour y (in cups) is proportional to the number x of eggs in a recipe. This means that for every 4 eggs, we use 6 cups of flour.

To represent this situation as an equation, we set up a proportion:

y / x = 6 / 4

Which simplifies to:

y / x = 3 / 2

We then solve this proportion to find the number of eggs (x) when we have 12 cups of flour (y).

12 / x = 3 / 2

Cross-multiplying gives us:

2 * 12 = 3 * x

24 = 3x

And by dividing both sides by 3, we find:

x = 8

Therefore, if the recipe uses 12 cups of flour, it includes 8 eggs.