06/03/2020 (2011: National Sprint Round, Problem 5)

Q: A student was supposed to substitute a certain value for x into the expression 2x³. The student thought the expression was (2x)³. If the student's answer was 384 greater than the correct answer, what value of x did the student use?

A: 4

We write an equation, with (2x)³ being what the student wrote and 2x³ being what the student was supposed to write. We solve it as shown below: