Use the table to answer the question.

Question

Cups of Flour Loaves of Bread
1 12
2 1
3 112
4 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

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Answer 1

To find the constant of proportionality for the bakery's recipe, we need to determine the ratio of cups of flour to loaves of bread. The recipe states that it requires 2 cups of flour for each loaf.

We can look through the data table:

• For 1 cup of flour, the bakery makes 12 loaves of bread: \( \frac{1}{12} \)
• For 2 cups of flour, the bakery makes 1 loaf of bread: \( \frac{2}{1} \)
• For 3 cups of flour, the bakery makes 112 loaves of bread: \( \frac{3}{112} \)
• For 4 cups of flour, the bakery makes 2 loaves of bread: \( \frac{4}{2} \)

The constant of proportionality can be represented by the formula \( \frac{\text{Cups of Flour}}{\text{Loaves of Bread}} \). We are looking for a scenario that matches the original recipe's requirement of 2 cups of flour for each loaf.

In the second pair (2 cups of flour and 1 loaf of bread), the values perfectly align with the proportionality of the recipe since \( 2 \text{ cups of flour} = 1 \text{ loaf of bread} \).

Thus, the ratio in that ordered pair where the constant of proportionality (2 cups of flour per loaf of bread) appears is:

(2, 1)