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

Answer 1

Let S be the original total: S = 112.75 + 76.85 + 134.50 + 89.65 = 413.75.

If item with price p is marked down 30% and the others are marked up 25%, the net change in total is
0.25*(S − p) − 0.30*p = 0.25S − 0.55p.

We want 0.25S − 0.55p = 29.46. Compute 0.25S = 103.4375, so
0.55p = 103.4375 − 29.46 = 73.9775 ⇒ p ≈ 73.9775/0.55 ≈ 134.50.

That matches the boots. Answer: c.