If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

Direct variation means y = kx for some constant k. The two given pairs imply 180 = kn and n = 5k, so k = n/5 and 180 = n²/5; therefore n² = 900. The positive value among the choices is n = 30, choice C, “30.” Strictly, n = −30 also satisfies the equations, so the question needs an assumption that n is positive for the answer to be unique.

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