A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 16 grams. The jeweler used 178 grams of gold and made 7 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.

The jeweler made 11 bracelets and 7 necklaces.

Step-by-step explanation:

Given that a jeweler had a fixed amount of gold to make bracelets and necklaces, and the amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 16 grams, knowing that the jeweler used 178 grams of gold and made 7 more necklaces than bracelets, to determine a system of equations that could be used to determine the number of bracelets made and the number of necklaces made, the following mathematical reasoning should be considered:

(16 - 6) x 7 = 70

178 - 70 = 108

108/6 = 18

18 - 7 = 11

(11 x 6) + (7 x 16) = X

66 + 112 = X

178 = X

Thus, the jeweler made 11 bracelets and 7 necklaces.