Final answer:
Julia will need 20 gallons of paint to cover her entire wall. This was calculated by setting up a proportion based on the amount used for 1/8th of the wall and finding the amount needed for the whole wall.
Step-by-step explanation:
To calculate how much paint is needed to cover Julia's entire wall, we need to set up a proportion since we know the amount of paint used for a part of the wall. Julia used 2 and 1/2 gallons of paint to cover 1/8 of her wall.
Let's convert 2 and 1/2 gallons to an improper fraction:
2 + 1/2 = 4/2 + 1/2 = 5/2 gallons of paint.
Now, we'll set up a proportion to find the total gallons needed for the whole wall (which is 8/8 since 8 times 1/8 equals the whole):
1/8 wall / 5/2 gallons = 8/8 wall / x gallons.
After cross-multiplying, we get:
1x = 8 * 5/2
x = 8 * 5/2 / 1
x = (8 * 5)/2
x = 40/2
x = 20 gallons.
Therefore, to cover the entire wall, Julia will need 20 gallons of paint. The correct answer is D - 20 gallons.
Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are key foundations to understand the various concepts in mathematics as well as in science.
Proportion finds application in solving many daily life problems such as in business while dealing with transactions or while cooking, etc. It establishes a relation between two or more quantities and thus helps in their comparison.