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Answer :
To solve this problem, we need to determine how many additional necklaces per day the jewelry maker must produce if she lowers her price from [tex]$18 to $[/tex]10 per necklace in order to maintain the same total earnings over a 6-day workweek.
Let's break it down step-by-step:
1. Calculate Current Weekly Earnings:
- Current price per necklace: [tex]$18
- Necklaces made per day: 15
- Days worked per week: 6
First, we calculate the current earnings per week by multiplying the number of necklaces made per day by the price per necklace and the number of days she works:
\[
\text{Current weekly earnings} = 18 \times 15 \times 6 = 1620
\]
So, her current weekly earnings are $[/tex]1620.
2. Determine Required Production at New Price:
- New price per necklace: [tex]$10
Next, to maintain the earnings of $[/tex]1620 at the new price of $10 necklace, we set up the equation:
[tex]\[
\text{New necklaces needed per week} = \frac{1620}{10} = 162
\][/tex]
3. Calculate New Daily Production Rate:
Since she works 6 days a week, we divide the total number of necklaces needed by the number of workdays:
[tex]\[
\text{New necklaces per day} = \frac{162}{6} = 27
\][/tex]
4. Calculate Increase in Production:
Finally, we compare the new production rate with the old rate to find the increase needed per day:
[tex]\[
\text{Increase in production per day} = 27 - 15 = 12
\][/tex]
Therefore, the jewelry maker must increase her production by 12 necklaces per day on average to maintain the same weekly earnings. The correct answer is (A) 12.
Let's break it down step-by-step:
1. Calculate Current Weekly Earnings:
- Current price per necklace: [tex]$18
- Necklaces made per day: 15
- Days worked per week: 6
First, we calculate the current earnings per week by multiplying the number of necklaces made per day by the price per necklace and the number of days she works:
\[
\text{Current weekly earnings} = 18 \times 15 \times 6 = 1620
\]
So, her current weekly earnings are $[/tex]1620.
2. Determine Required Production at New Price:
- New price per necklace: [tex]$10
Next, to maintain the earnings of $[/tex]1620 at the new price of $10 necklace, we set up the equation:
[tex]\[
\text{New necklaces needed per week} = \frac{1620}{10} = 162
\][/tex]
3. Calculate New Daily Production Rate:
Since she works 6 days a week, we divide the total number of necklaces needed by the number of workdays:
[tex]\[
\text{New necklaces per day} = \frac{162}{6} = 27
\][/tex]
4. Calculate Increase in Production:
Finally, we compare the new production rate with the old rate to find the increase needed per day:
[tex]\[
\text{Increase in production per day} = 27 - 15 = 12
\][/tex]
Therefore, the jewelry maker must increase her production by 12 necklaces per day on average to maintain the same weekly earnings. The correct answer is (A) 12.
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