If one quart of paint is exactly enough for two coats of paint on a 9-foot by 10-foot wall, how many quarts of paint are needed to apply one coat of paint to a 10-foot by 12-foot w... If one quart of paint is exactly enough for two coats of paint on a 9-foot by 10-foot wall, how many quarts of paint are needed to apply one coat of paint to a 10-foot by 12-foot wall? Express your answer as a common fraction.
Understand the Problem
The problem states that one quart of paint covers a 9-foot by 10-foot wall with two coats. We need to find out how much paint is needed for a 10-foot by 12-foot wall with only one coat. This involves calculating areas and scaling the paint quantity accordingly.
Answer
$\frac{2}{3}$ quart
Answer for screen readers
$\frac{2}{3}$ quart
Steps to Solve
- Calculate the area of the first wall
The first wall is 9 feet by 10 feet, so its area is:
$Area_1 = 9 \text{ ft} \times 10 \text{ ft} = 90 \text{ ft}^2$
- Determine the area covered by one quart with two coats
One quart covers the $90 \text{ ft}^2$ wall with two coats.
- Calculate the effective coverage area of one quart for one coat
Since one quart covers the area with two coats, we can infer that one quart would cover twice the area with only one coat.
$EffectiveArea = 90 \text{ ft}^2 \times 2 = 180 \text{ ft}^2$
One quart covers $180 \text{ ft}^2$ with one coat
- Calculate the area of the second wall
The second wall is 10 feet by 12 feet, so its area is:
$Area_2 = 10 \text{ ft} \times 12 \text{ ft} = 120 \text{ ft}^2$
- Determine the amount of paint needed for the second wall
To find out how many quarts are needed for the second wall, we divide the area of the second wall by the effective area covered by one quart of paint with one coat:
$QuartsNeeded = \frac{Area_2}{EffectiveArea} = \frac{120 \text{ ft}^2}{180 \text{ ft}^2} = \frac{2}{3}$
Therefore, $\frac{2}{3}$ of a quart of paint is needed for the second wall.
$\frac{2}{3}$ quart
More Information
The problem involves proportional reasoning and area calculations. It's typical to encounter such problems when dealing with scaling quantities in real-world scenarios, like painting or construction.
Tips
A common mistake is forgetting to account for the two coats of paint on the first wall. Many people may directly relate the area of the first wall to the amount of paint needed for the second wall without adjusting for coverage. Forgetting to convert the coverage area from two coats to one coat will lead to an incorrect answer. Another mistake is miscalculating the areas of the walls.
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