Question

Alice has 3/4 of a gallon of paint. She figures that she can paint 2/3 of her living room wall with this amount of paint. How much paint does she need to paint the whole wall? Explain your thinking.

a) 1/4 gallon
b) 1/2 gallon
c) 3/8 gallon
d) 5/12 gallon

Answer 1

Alice needs 1 1/8 gallons of paint to cover the whole wall. The correct amount of paint is not listed among the given options a) through d). Given the direct proportionality between gallons of paint and the wall area covered, none of the provided options are correct.

Step-by-step explanation:

Alice has 3/4 of a gallon of paint, and she can paint 2/3 of her living room wall with it. To find how much paint she would need to paint the whole wall, we set up a proportion where the amount of paint is directly proportional to the area of the wall she can cover. So, if 3/4 gallon is to 2/3 of a wall, then X gallon (the amount we are looking for) is to 1 wall (the whole wall).

We can write this as: (3/4) / (2/3) = X / 1. To solve for X, we can cross multiply to get 3/4 = 2X/3. After cross multiplying, we have 3 * 3 = 4 * 2X, which simplifies to 9 = 8X. Finally, divide both sides by 8 to solve for X, getting X = 9/8 or 1 1/8 gallons.

Since we are only given options a) through d), none of which equal 1 1/8 gallons, and the actual amount Alice needs is none of the options, it's possible there is either an error in the provided options, or additional contextual information is required to arrive at one of those as a correct answer. However, given only the information provided in the question, the correct amount of paint needed to cover the whole wall is 1 1/8 gallons.