To fill and art exhibit, the students in an art course are assigned to create one epiece of artwork each in the following distribution: 1andfrasl;3 are sculptures, 1andfrasl;8 are oil paintings, 1andfrasl;2 are watercolors and the remaining 10 pieces are mosaics. How many students are in the art class?a)80b)120c)240d)320e)400Correct answer is option 'C'. Can you explain this answer?

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To fill and art exhibit, the students in an art course are assigned to create one epiece of artwork each in the following distribution: 1⁄3 are sculptures, 1⁄8 are oil paintings, 1⁄2 are watercolors and the remaining 10 pieces are mosaics. How many students are in the art class?

a)
80
b)
120
c)
240
d)
320
e)
400

Correct answer is option 'C'. Can you explain this answer?

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To fill and art exhibit, the students in an art course are assigned to...

Step 1: Analyze the Question
In this question, we are presented with a series of parts that make up the whole- in this case, the number of students in an art class. Notice that most of the whole is identified as fractions of the whole, while one part is identified as a specific quantity. We can use this to our advantage.

Step 2: State the Task
Determine the sum of the fractions in the question stem (sculptures, oil paintings, watercolors), since this makes up all but one part of the whole number of students. Subtracting this fraction from 1 will provide the fraction of the whole that is the remaining part (mosaics). Finally, we will solve for the number of students in the class. Note that this question can also be solved by Backsolving, since all of the answer choices are numbers and we can test out the answer choices to see if 10 pieces remain after calculating the number of other pieces of artwork.

Step 3: Approach Strategically
We are told that ¹/₃ of the students create sculptures, ¹/₈ create oil paintings, ¹/₂ create watercolors, and the remaining 10 pieces are mosaics. Let's assume that the total number of students in the class is x. Then the sum of the sculptures, oil paintings, and watercolors is as follows:

(¹/₃)x + (¹/₈)x + (¹/₂)x = x(¹/₃ + ¹/₈ + ¹/₂) = x(⁸/₂₄ + ³/₂₄ + ¹²/₂₄) = x(²³/₂₄)

So the sum of the sculptures, oil paintings, and watercolors is ²³/₂₄ of the art in the exhibit. Therefore. the remaining 10 pieces must be 1-²³/₂₄ = ¹/₂₄ of the total pieces. We can set up the equation:

(¹/₂₄)x = 10; x= 240

Choice (C) is correct.

Step 4: Confirm Your Answer
Plug your value for x into the original equation to confirm your calculations are correct.

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