Question

A jeweler makes necklaces. One day, he used 4 sets of pearls and 7 sets of diamonds to make a total of 33 necklaces. On the second day, he used 2 sets of pearls and 7 sets of diamonds to make a total of 27 necklaces. Write a system of equations, then determine how many pearls and how many diamonds were used for each necklace.

Answer 1

The jeweler uses 3 pearls and 3 diamonds for each necklace, which we found by setting up a system of equations based on the given information and solving for the unknowns.

Step-by-step explanation:

To solve the problem presented, we must set up a system of equations where the number of pearls used per necklace is represented by P, and the number of diamonds used per necklace is represented by D. The two equations representing day one and day two, based on the number of sets used and necklaces made, are as follows:

1. 4P + 7D = 33
2. 2P + 7D = 27

To determine the number of pearls (P) and diamonds (D) used for each necklace, we can subtract the second equation from the first, which gives us:

2P = 6

This implies that P, the number of pearls used per necklace, is 3. To find the number of diamonds D, we can substitute P back into either equation, let's use the second one:

2(3) + 7D = 27

6 + 7D = 27

7D = 21

D = 3

Therefore, the jeweler uses 3 pearls and 3 diamonds for each necklace.