ExplanationHelen bought a ticket for $252; if she had bought it one day later, she would have paid $54 more. There are three possibilities that represent the dividing lines between the given discount levels:

Possibility 1: She bought the ticket 60 days in advance for a 40% discount (if she’d bought it one day later, or 59 days in advance, she would have received a 30% discount instead).

Possibility 2: She bought the ticket 30 days in advance for a 30% discount (if she’d bought it one day later, or 29 days in advance, she would have received a 15% discount instead).

Possibility 3: She bought the ticket 5 days in advance for a 15% discount (if she’d bought it one day later, or 4 days in advance, she would not have received any kind of discount).

This question is harder than it looks, do not calculate a percent change between $252 and $306. The discounts are percents of the full-price ticket, which is an unknown value. Call it x.

Note that the only three possible answers are 5, 30, and 60 (answers (A), (B), and (D), respectively); 59 days ahead and 89 days ahead do not represent days for which the next day (58 and 88 days ahead, respectively) results in a change in the discount.

Possibility 1 (60 days in advance): $252 would represent a 40% discount from the original price, so the original price would be $252 = 0.6x, and x would be $420.

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Sandy

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