Question

Lena is creating beaded jewelry to give to her family and friends. For her family, she assembled 6 bracelets and 5 necklaces, using a total of 526 beads. For her friends, she assembled 6 bracelets and 2 necklaces, using a total of 286 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?

Answer 1

Using a system of equations, we find that Lena uses 21 beads for each bracelet and 80 beads for each necklace.

Step-by-step explanation:

To determine the number of beads Lena uses for each bracelet and each necklace, we can set up a system of equations based on the information provided. Let x be the number of beads used for each bracelet and let y be the number of beads used for each necklace.

For the family jewelry, Lena made 6 bracelets and 5 necklaces using a total of 526 beads. This gives us the first equation:
6x + 5y = 526

For her friends, she made 6 bracelets and 2 necklaces with a total of 286 beads, giving us the second equation:
6x + 2y = 286

Subtracting the second equation from the first eliminates the x variable:
5y - 2y = 526 - 286
3y = 240
Dividing by 3 yields:
y = 80

Now, replace y with 80 in either original equation to solve for x. Using the second equation:
6x + 2(80) = 286
6x + 160 = 286
6x = 126
Dividing by 6 yields:
x = 21

Therefore, Lena uses 21 beads for each bracelet and 80 beads for each necklace.