Question

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 16 grams. The jeweler used 130 grams of gold and made 5 more bracelets than necklaces. 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.

Answer 1

Let's use the variables B for the number of bracelets made and N for the number of necklaces made.

From the problem, we know that the amount of gold used can be determined by multiplying the number of bracelets made by 5 and the number of necklaces made by 16, so we have the equation:

5B + 16N = 130

We also know that the number of bracelets made is 5 more than the number of necklaces made, so we have the equation:

B = N + 5

Thus, the system of equations that could be used to determine the number of bracelets made and the number of necklaces made is:

5B + 16N = 130
B = N + 5