Question
Every Sunday, Will and his cousins get together for brunch. This week, Will is in charge of making fresh-squeezed orange juice.
There is a proportional relationship between the number of oranges Will squeezes, x, and the amount of juice (in ounces) he makes, y.
x (oranges) y (ounces)
16 48
22 66
23 69
25 75
What is the constant of proportionality? Write your answer as a whole number or decimal.
ounces per orange
There is a proportional relationship between the number of oranges Will squeezes, x, and the amount of juice (in ounces) he makes, y.
x (oranges) y (ounces)
16 48
22 66
23 69
25 75
What is the constant of proportionality? Write your answer as a whole number or decimal.
ounces per orange
Answers
GPT-4o mini
To find the constant of proportionality in the relationship between the number of oranges squeezed (x) and the amount of juice produced (y), we can use the formula for the constant of proportionality, which is:
\[
k = \frac{y}{x}
\]
We'll calculate \(k\) for each pair of values given in the table.
1. For \(x = 16\) and \(y = 48\):
\[
k = \frac{48}{16} = 3
\]
2. For \(x = 22\) and \(y = 66\):
\[
k = \frac{66}{22} = 3
\]
3. For \(x = 23\) and \(y = 69\):
\[
k = \frac{69}{23} = 3
\]
4. For \(x = 25\) and \(y = 75\):
\[
k = \frac{75}{25} = 3
\]
In each case, the constant of proportionality \(k\) is 3.
Thus, the constant of proportionality, or ounces per orange, is:
\[
\boxed{3}
\]
\[
k = \frac{y}{x}
\]
We'll calculate \(k\) for each pair of values given in the table.
1. For \(x = 16\) and \(y = 48\):
\[
k = \frac{48}{16} = 3
\]
2. For \(x = 22\) and \(y = 66\):
\[
k = \frac{66}{22} = 3
\]
3. For \(x = 23\) and \(y = 69\):
\[
k = \frac{69}{23} = 3
\]
4. For \(x = 25\) and \(y = 75\):
\[
k = \frac{75}{25} = 3
\]
In each case, the constant of proportionality \(k\) is 3.
Thus, the constant of proportionality, or ounces per orange, is:
\[
\boxed{3}
\]