Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Samantha is creating beaded jewelry to give to her family and friends. For her family, she assembled 5 bracelets and 2 necklaces, using a total of 221 beads. For her friends, she assembled 9 bracelets and 4 necklaces, using a total of 423 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?

Answer 1

We have to calculate the number of beads she uses for every bracelet and for every necklace.

Let B the beads for each bracelet and N the beads for each necklace.

For her family, she assembled 5 bracelets and 2 necklaces, using a total of 221 beads. We can represent this as:

$5B+2N=221$

For her friends, she assembled 9 bracelets and 4 necklaces, using a total of 423 beads. This can be represented as:

$9B+4N=423$

We can solve this by elimination, by substracting two times the first equation from the second equation:

$\begin{gathered} (9B+4N)-2(5B+2N)=423-2(221) \\ 9B+4N-10B-4N=423-442 \\ -1B+0N=-19 \\ B=19 \end{gathered}$

We can now use any of the equations to find the value of N:

$\begin{gathered} 9B+4N=423 \\ 9(19)+4N=423 \\ 171+4N=423 \\ 4N=423-171 \\ 4N=252 \\ N=\frac{252}{4} \\ N=63 \end{gathered}$

Answer: She uses 19 beads for each bracelet and 63 beads for each necklace.