Question

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.

Answer 1

Let x represent number of bracelets and y represent number of necklaces.

We have been given that a jeweler made 7 more necklaces than bracelets. This means that number of necklaces will be $x+7$. We can represent this information in an equation as:

$y=x+7...(1)$

We have been given that the amount of gold in each bracelet is 6 grams, so amount used for x bracelets would be $6x$ grams.

We are also told that the amount of gold in each necklace is 16 grams, so amount used for y necklaces would be $16y$ grams.

Since the jeweler used 178 grams of gold, so we will equate the amount of gold used in x bracelets and y necklaces with 178 as:

$6x+16y=178...(2)$

Therefore, our required system of equations would be:

$y=x+7...(1)$

$6x+16y=178...(2)$