Question

Ashley runs a hardware store. She has decided to apply a markdown of 15% to one item in order to draw customers into the store, and she will apply a markup of 10% to three different items, which she hopes the customers will purchase after purchasing the marked-down item. She has chosen four candidates for this process: a power drill with an initial price of $51.49, a ceiling fan with an initial price of $64.79, a miniature circular saw with an initial price of $45.99, and a screwdriver set with an initial price of $37.39. After applying the changes, the total cost of purchasing one of each item is $3.77 more than it was before applying the changes. Which item was marked down?
a.
power drill
b.
ceiling fan
c.
circular saw
d.
screwdriver set

Answer 1

Let the marked-down item's price be p. Original total = 51.49 + 64.79 + 45.99 + 37.39 = 199.66.

New total = 0.85p + 1.10(199.66 − p) = 1.10·199.66 − 0.25p.
Increase = new − original = 0.10·199.66 − 0.25p = 19.966 − 0.25p.

Set this equal to 3.77:
19.966 − 0.25p = 3.77 → 0.25p = 16.196 → p = 64.784 ≈ 64.79.

That matches the ceiling fan. Answer: b.