Question

A city has two paint supply stores. Store A sells 3-gallon containers of paint. Each container covers 1044 square feet for $111. Store B sells paint only by the quart. Each quart sells for $9.25 and covers 87 square feet. At each store, the cost of paint is in a proportional relationship to the amount. Find the constant of proportionality for Store A. At which store is paint a better buy?

Answer 1

The constant of proportionality for Store A is approximately 9.41 square feet per dollar, calculated by dividing the coverage by the cost. Store B has an identical constant of proportionality. Thus, both stores offer the same value for paint in terms of coverage per dollar.

Step-by-step explanation:

The constant of proportionality for Store A can be calculated by dividing the coverage of paint by cost. Since Store A sells 3-gallon containers that cover 1044 square feet for $111, to find the constant of proportionality, you divide 1044 square feet by $111, which gives you approximately 9.41 square feet per dollar.

To determine which store offers a better buy, you would compare the constants of proportionality for both stores. Store B sells paint by the quart and each quart covers 87 square feet and costs $9.25, which gives us a constant of proportionality of approximately 9.41 square feet per dollar (same as Store A).

Since the constants of proportionality are identical for both stores, neither store has a better buy over the other based on this metric alone. If other factors such as quality, brand, or convenience are equal, a customer could choose either store without a cost difference in terms of coverage per dollar.