A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 7 grams and the amount of gold in each necklace is 24 grams. The jeweler used 172 grams of gold and made 2 more necklaces than bracelets. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you use to write the system.

To solve the problem, we will define two variables:

• Let \( b \) be the number of bracelets made.
• Let \( n \) be the number of necklaces made.

Based on the information provided, we can set up the following system of equations:

1. The total amount of gold used for bracelets and necklaces can be represented by the equation: \[ 7b + 24n = 172 \] This equation states that the total weight of gold used (7 grams per bracelet and 24 grams per necklace) adds up to 172 grams.

2. The problem states that the jeweler made 2 more necklaces than bracelets, which gives us the second equation: \[ n = b + 2 \] This equation indicates that the number of necklaces is 2 more than the number of bracelets.

Thus, the complete system of equations is: \[ \begin{cases} 7b + 24n = 172 \ n = b + 2 \end{cases} \]

This system can be used to determine the number of bracelets and necklaces made by the jeweler.