Question

a new homeowner is painting the walls of a room. the walls have a total area of 253 square feet. a quart of paint covers 46 square feet. if paint is sold quarts are needed?

1. understand the problem. reread it as many times as needed.

which sentence below describes the solution to this problem?
a. the area being painted is the area covered by a quart divided by the number of quarts needed, rounded up to the nearest square foot.
b. the number of quarts needed is the area being painted divided by the area covered by a quart, rounded up to the nearest whole quart.
c. the number of quarts needed is the area covered by a quart divided by the area being painted, rounded up to the nearest whole quart.
d. the area being painted is the number of quarts needed divided by the area covered by a quart, rounded up to the nearest square foot.

1. translate into an equation. substitute the values for the number of square feet being painted and the square feet covered by a quart below.

number of quarts is square feet divided by square feet per quart
number of quarts = +

Explanation:

Part 1 (Multiple Choice)

To determine the number of quarts needed, we use the formula: \(\text{Number of quarts} = \frac{\text{Total area to paint}}{\text{Area covered per quart}}\). Since we can't buy a fraction of a quart (we need to cover the entire area), we round up to the nearest whole quart.

• Option A: Incorrect. The area being painted is not calculated by dividing the area per quart by the number of quarts.
• Option B: Correct. This matches the formula \(\text{Number of quarts} = \frac{\text{Area being painted}}{\text{Area covered by a quart}}\) with rounding up.
• Option C: Incorrect. Dividing the area per quart by the total area would give a value less than 1, which doesn't make sense for the number of quarts.
• Option D: Incorrect. The area being painted is not calculated by dividing the number of quarts by the area per quart.

Step 1: Identify the values

The total area to paint (square feet) is 253, and the area covered per quart (square feet per quart) is 46.

Step 2: Substitute into the equation

The equation is \(\text{number of quarts} = \frac{\text{square feet}}{\text{square feet per quart}}\). Substituting the values, we get \(\text{number of quarts} = \frac{253}{46}\).

Answer:

B. The number of quarts needed is the area being painted divided by the area covered by a quart, rounded up to the nearest whole quart.

Part 2 (Equation Substitution)