Quantity A
Quantity B
Both quantities can be simplified to
. The two quantities are equal.
54.
(B).
Helen 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 1 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 1 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 1 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 = 0.6
x
, and
x
would be
$420.
If the full ticket price is $420, then buying the ticket 1 day later would result
in a 30% discount instead, or ($420)(0.7) = $294. The problem indicates,
however, that Helen would have paid $306, so Possibility 1 is not correct.
Possibility 2 (30 days in advance): $252 would represent a 30% discount from
the original price, so the original price would be $252 = 0.7
x
and
x
would be
$360.
If the full ticket price is $360, then buying the ticket 1 day later would result
in a 15% discount instead, or ($360)(0.85) = $306. This matches the figure
given in the problem, so Possibility 2 is correct; you do not need to test
Possibility 3. Helen bought the ticket 30 days in advance.
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