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A certain store marks down a watch by $20 \%$ each month it isn't sold
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22 Aug 2025, 23:42
22 Aug 2025, 23:42
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Question Stats:
100% (03:27) correct
0% (00:00) wrong based on 2 sessions
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A certain store marks down a watch by $\(20\) %$ each month it isn't sold. If the watch costs \(\$40\) on January 1, what does the watch cost on June 1?
Round to the nearest cent.
Round to the nearest cent.
Show: ::
13.11
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Re: A certain store marks down a watch by $20 \%$ each month it isn't sold
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31 Aug 2025, 10:12
31 Aug 2025, 10:12
Expert Reply
The watch costs $\(\$ 40\)$ on January 1 , and it is marked down by $\(20\) %$ each month it isn't sold.
To find the cost on June 1, which is 5 months later (January to June is 5 months):
Step 1: Calculate month-by-month decrease by 20%
Each month, the price is $80 %$ ( $100 %-20 %$ ) of the previous month's price.
After $n$ months, price:
$$
\(P_n=P_0 \times(0.8)^n\)
$$
where $\(P_0=40, n=5\)$.
Step 2: Calculate price on June 1
$$
\(P_5=40 \times(0.8)^5=40 \times 0.32768=13.1072\)
$$
Step 3: Round to nearest cent
$$
\(P_5 \approx \$ 13.11\)
$$
Final Answer:
On June 1, the watch costs approximately $\(\$ 13.11\)$.
To find the cost on June 1, which is 5 months later (January to June is 5 months):
Step 1: Calculate month-by-month decrease by 20%
Each month, the price is $80 %$ ( $100 %-20 %$ ) of the previous month's price.
After $n$ months, price:
$$
\(P_n=P_0 \times(0.8)^n\)
$$
where $\(P_0=40, n=5\)$.
Step 2: Calculate price on June 1
$$
\(P_5=40 \times(0.8)^5=40 \times 0.32768=13.1072\)
$$
Step 3: Round to nearest cent
$$
\(P_5 \approx \$ 13.11\)
$$
Final Answer:
On June 1, the watch costs approximately $\(\$ 13.11\)$.
Re: A certain store marks down a watch by $20 \%$ each month it isn't sold
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04 Sep 2025, 13:51
04 Sep 2025, 13:51
Yeah, the key is to think in terms of the remaining percentage each month instead of just subtracting. So you multiply by 0.8 each time. After 5 months, it comes out to about $13.11, just like Carcass explained.
It actually reminds me of how seasonal items drop in value if they sit too long. I noticed the same thing when browsing inflatables for an event — prices go down over time, but so does availability.
It actually reminds me of how seasonal items drop in value if they sit too long. I noticed the same thing when browsing inflatables for an event — prices go down over time, but so does availability.
