At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $2.40 and a 16-ounce cup costs $3.20.

Question

Is the linear relationship between cup size and cost also proportional? Why or why not?
Yes, there is no constant of proportionality.
No, the constant of proportionality is 0.2.
Yes, the constant of proportionality is 0.2.
No, there is no constant of proportionality.

Answer 1

To determine whether the relationship between cup size and cost is proportional, we'll first check if there is a constant of proportionality.

A relationship is proportional if the ratio of the cost to the size (in ounces) is constant for both cup sizes.

For the 12-ounce cup: \[ \text{Cost per ounce} = \frac{$2.40}{12 \text{ oz}} = 0.20 \text{ dollars per ounce} \]

For the 16-ounce cup: \[ \text{Cost per ounce} = \frac{$3.20}{16 \text{ oz}} = 0.20 \text{ dollars per ounce} \]

Since both cup sizes yield the same cost per ounce of $0.20, the relationship appears linear, and there is a constant of proportionality.

Thus, the correct answer is:

Yes, the constant of proportionality is 0.2.