Question

At the Greenpoint Summer Festival, Farid is selling his animal-shaped cupcakes. Farid had to buy the ingredients and pay a food-vendor fee, so he hopes he sells enough cupcakes to make a profit.
This table shows the relationship between the number of cupcakes Farid sells, x, and the amount of profit (in dollars) he'll make, y.
x (cupcakes) y (dollars)
52 $34
54 $42
63 $78
66 $90
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine if \( x \) (the number of cupcakes) and \( y \) (the profit) have a proportional relationship, we need to check if the ratios \(\frac{y}{x}\) are constant for all pairs of \((x, y)\).

Let's calculate the ratios for the given points:

1. For \( x = 52 \) and \( y = 34 \):
\[
\frac{y}{x} = \frac{34}{52} \approx 0.6538
\]

2. For \( x = 54 \) and \( y = 42 \):
\[
\frac{y}{x} = \frac{42}{54} \approx 0.7778
\]

3. For \( x = 63 \) and \( y = 78 \):
\[
\frac{y}{x} = \frac{78}{63} = 1.2381
\]

4. For \( x = 66 \) and \( y = 90 \):
\[
\frac{y}{x} = \frac{90}{66} \approx 1.3636
\]

Since the ratios are not constant (they are approximately 0.6538, 0.7778, 1.2381, and 1.3636), we conclude that \( x \) and \( y \) do not have a proportional relationship.

Therefore, the answer is **no**.