Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Jennifer is creating beaded jewelry to give to her family and friends. For her family, she assembled 2 bracelets and 6 necklaces, using a total of 396 beads. For her friends, she assembled 5 bracelets and 5 necklaces, using a total of 370 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each? Jennifer uses beads for each bracelet and beads for each necklace.

Question

GPT 3.5 · Answer

Let x be the number of beads for each bracelet and y be the number of beads for each necklace.

For Jennifer's family:
2x + 6y = 396

For Jennifer's friends:
5x + 5y = 370

Now, we can solve this system of equations using elimination method:

First, multiply the second equation by 2:
10x + 10y = 740

Now, subtract the first equation from the new equation:
10x + 10y - (2x + 6y) = 740 - 396
8x + 4y = 344

Now, divide both sides by 4 to simplify:
2x + y = 86

Now, we have a new system of equation:
2x + y = 86
10x + 10y = 740

Now, let's multiply the first equation by 10 and then subtract it from the second equation:
20x + 10y - (10x + 10y) = 860 - 740
10x = 120
x = 12

Now, substitute x back into the first equation to solve for y:
2(12) + y = 86
24 + y = 86
y = 62

Therefore, Jennifer uses 12 beads for each bracelet and 62 beads for each necklace.