To calculate how much money Madame Dubois made, we can follow these steps:
1. Initial Information:
- The total number of pearl necklaces: [tex]\( 20 \)[/tex]
- The total cost of 20 pearl necklaces: [tex]\( \$500 \)[/tex]
2. Calculating the number of necklaces sold at \[tex]$40 each:
Madame Dubois sold \( \frac{3}{4} \) of her necklaces at \$[/tex]40 each.
[tex]\[
\frac{3}{4} \text{ of } 20 = \frac{3}{4} \times 20 = 15 \text{ necklaces}
\][/tex]
3. Earnings from the necklaces sold at \[tex]$40 each:
Selling price per necklace: \( \$[/tex]40 \)
[tex]\[
\text{Earnings from 15 necklaces} = 15 \times 40 = \$600
\][/tex]
4. Calculating the number of necklaces remaining:
Total necklaces: [tex]\( 20 \)[/tex]
Necklaces sold at \[tex]$40: \( 15 \)
\[
\text{Necklaces remaining} = 20 - 15 = 5
\]
5. Calculating the cost price per necklace:
Total cost of 20 necklaces: \( \$[/tex]500 \)
[tex]\[
\text{Cost price per necklace} = \frac{500}{20} = \$25
\][/tex]
6. Earnings from the remaining necklaces sold at cost price:
Number of remaining necklaces: [tex]\( 5 \)[/tex]
Cost price per necklace: [tex]\( \$25 \)[/tex]
[tex]\[
\text{Earnings from 5 necklaces} = 5 \times 25 = \$125
\][/tex]
7. Calculating the total earnings:
[tex]\[
\text{Total earnings} = \text{Earnings from necklaces sold at \$40 each} + \text{Earnings from remaining necklaces}
\][/tex]
[tex]\[
\text{Total earnings} = \$600 + \$125 = \$725
\][/tex]
Madame Dubois made a total of \$725 from selling all her pearl necklaces.
