Cups of flour and loaves of bread
1 1/2
2 1
3 1 1/2
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.
The ratio with the constant of proportionality can be determined by dividing the number of loaves of bread by the amount of flour needed for that number of loaves.
For example, for the first ratio (1, 1/2), we divide the number of loaves (1) by the amount of flour needed (1/2).
1 ÷ 1/2 = 2
So, the ratio with the constant of proportionality is (1, 2).
To find the constant of proportionality, we need to find the ratio of the number of cups of flour to the number of loaves of bread.
Let's look at the data table:
Cups of flour and loaves of bread
1 1/2
2 1
3 1 1/2
4 2
The ratio of cups of flour to loaves of bread for each entry in the table are as follows:
(1/2) / 1 = 1/2
1 / 2 = 1/2
(3/2) / 3 = 1/2
2 / 4 = 1/2
As we can see, the ratio of cups of flour to loaves of bread is always 1/2.
Therefore, the constant of proportionality appears at the ratio (1/2, 1).
To identify the constant of proportionality in the data table, we need to compare the number of loaves of bread with the corresponding amount of flour needed.
Let's divide the amount of flour by the number of loaves for each entry in the table:
For the first row, we have 1 1/2 cups of flour for 1 loaf of bread. Therefore, the ratio is 1 1/2 divided by 1, which equals 1 1/2.
For the second row, we have 2 cups of flour for 2 loaves of bread. The ratio is 2 divided by 2, which equals 1.
For the third row, we have 3 1/2 cups of flour for 3 loaves of bread. The ratio is 3 1/2 divided by 3, which equals 1 1/2.
For the fourth row, we have 4 cups of flour for 4 loaves of bread. The ratio is 4 divided by 4, which equals 1.
To determine the constant of proportionality, we need to find a ratio that is consistent throughout all the entries in the table. From the calculations above, we can see that the ratio 1 appears twice: once in the second row (2 cups of flour for 2 loaves of bread) and again in the fourth row (4 cups of flour for 4 loaves of bread).
Therefore, the constant of proportionality appears at the ratio (2, 1) in the data table.