Question

Craig runs a clothing store. He has decided to apply a markdown of 30% to one item in order to draw customers into the store, and he will apply a markup of 25% to three different items, which he hopes the customers will purchase after purchasing the marked-down item. He has chosen four candidates for this process: a leather jacket with an initial cost of $112.75, a blazer with an initial cost of $76.85, a pair of boots with an initial cost of $134.50, and a wristwatch with an initial price of $89.65. After applying the changes, the total cost of purchasing one of each item is $29.46 more than it was before applying the changes. Which item was marked down?
a.
wristwatch
b.
leather jacket
c.
boots
d.
blazer


Please select the best answer from the choices provided

A
B
C
D

Answer 1

C

Let S = 112.75 + 76.85 + 134.50 + 89.65 = 413.75. If x is the marked-down item, new total T = 0.7x + 1.25(S − x) = 1.25S − 0.55x.
So T − S = 0.25S − 0.55x = 29.46. Plugging S gives 0.55x = 0.25·413.75 − 29.46 = 73.975, so x = 73.975/0.55 = 134.50.
Therefore the boots were marked down (choice C).