1. **State the problem:** A jeweler has a fixed amount of gold and makes bracelets and necklaces. Each bracelet uses 7 grams of gold, each necklace uses 18 grams, and the total gold used is 82 grams. The jeweler made a total of 7 items (bracelets + necklaces). We need to find how many bracelets and necklaces were made. 2. **Define variables:** Let $b$ be the number of bracelets and $n$ be the number of necklaces. 3. **Write the equations:** - Total items: $$b + n = 7$$ - Total gold used: $$7b + 18n = 82$$ 4. **Solve the system:** From the first equation, express $b$ as $$b = 7 - n$$ 5. Substitute into the second equation: $$7(7 - n) + 18n = 82$$ 6. Simplify: $$49 - 7n + 18n = 82$$ $$49 + 11n = 82$$ 7. Solve for $n$: $$11n = 82 - 49$$ $$11n = 33$$ $$n = 3$$ 8. Find $b$: $$b = 7 - 3 = 4$$ 9. **Answer:** The jeweler made 4 bracelets and 3 necklaces.