Question
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.
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
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
Answers
GPT-4o mini
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**.
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**.
Related Questions
Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profi...
Danielle likes to work alone and has strong math and analysis skills. She likes the challenges of th...
Daniella likes to purchase Adam's at estate sales clean them off then resell them online for a profi...
Danielle is a cosmetologist who specializes in hair color. What skill might benefit Danielle in her...