Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.

Question

To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?

Responses
A purchase price: $117, advertised price: $293purchase price: $117, advertised price: $293
B purchase price: $120, advertised price: $300purchase price: $120, advertised price: $300
C purchase price: $130, advertised price: $325purchase price: $130, advertised price: $325
D purchase price: $108, advertised price: $270purchase price: $108, advertised price: $270

Answer 1

Let \( x \) be the purchase price of the antique dresser.

According to the problem, Danielle advertised the dresser for 250% of her purchase price. Therefore, the advertised price can be expressed as:

\[ \text{Advertised Price} = 2.5 \times x = 2.5x \]

She sold the dresser for $255, which was 15% less than the advertised price. This means:

\[ 255 = (1 - 0.15) \times \text{Advertised Price} \]

Simplifying the equation for the advertised price:

\[ 255 = 0.85 \times \text{Advertised Price} \]

Thus:

\[ \text{Advertised Price} = \frac{255}{0.85} = 300 \]

Now, substituting back to find the purchase price:

\[ 2.5x = 300 \]

Dividing both sides by 2.5 gives:

\[ x = \frac{300}{2.5} = 120 \]

Therefore, Danielle purchased the antique dresser for $120 and her initial advertised price was $300.

The correct response is:

B: purchase price: $120, advertised price: $300.