Question

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.

Explanation:

Step1: Define variables

Let \( b \) = number of bracelets, \( n \) = number of necklaces.

Step2: Gold total equation

Gold from bracelets + gold from necklaces = total gold: \( 7b + 24n = 172 \)

Step3: Quantity relation equation

Necklaces = bracelets + 2: \( n = b + 2 \)

Answer:

Let \( b = \) number of bracelets, Let \( n = \) number of necklaces; System: \( 7b + 24n = 172 \), \( n = b + 2 \)