A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 12 bracelets and necklaces using 155 grams of gold. Determine the number of bracelets made and the number of necklaces made.

To determine the number of bracelets and necklaces the jeweler made, let's set up and solve a system of equations based on the information provided. ### Let: - \( b \) = number of bracelets - \( n \) = number of necklaces ### Given: 1. **Total items made:** \( b + n = 12 \) (The jeweler made a total of 12 bracelets and necklaces.) 2. **Total gold used:** \( 5b + 24n = 155 \) (Each bracelet uses 5 grams of gold and each necklace uses 24 grams of gold, totaling 155 grams.) ### Solving the Equations: 1. **From the first equation:** \( b = 12 - n \) 2. **Substitute \( b \) into the second equation:** \( 5(12 - n) + 24n = 155 \) \( 60 - 5n + 24n = 155 \) \( 19n + 60 = 155 \) \( 19n = 95 \) \( n = 5 \) 3. **Find \( b \):** \( b = 12 - n = 12 - 5 = 7 \) ### **Conclusion:** - **Number of Bracelets Made:** 7 - **Number of Necklaces Made:** 5