Let x be the profit of a bracelet and y the profit of a necklace.
Yesterday she sold: 9 bracelets and 3 necklaces, for a profit of $144:
[tex]9x+3y=144[/tex]
Today, she made a profit of $279 by selling 10 bracelets and 9 necklaces:
[tex]10x+9y=279[/tex]
System of equations:
[tex]\begin{gathered} 9x+3y=144 \\ 10x+9y=279 \end{gathered}[/tex]
To solve by elimination:
1. Multiply the first equation by -3:
[tex]\begin{gathered} -3(9x+3y=144 \\ \\ -27x-9y=-432 \end{gathered}[/tex]
2. Add equation you get in step 1 and the second equation in the system:
[tex]-17x=-153[/tex]
3. Use the equation you get in step 2 to solve x:
[tex]\begin{gathered} \text{Divide both sides of the equation into -17} \\ \\ \frac{-17}{-17}x=\frac{-153}{-17} \\ \\ x=9 \end{gathered}[/tex]
4. Use the value of x to solve y:
[tex]\begin{gathered} 9x+3y=144 \\ \\ 9(9)+3y=144 \\ 81+3y=144 \\ \\ \text{Subtract 81 in both sides of the equation:} \\ 81-81+3y=144-81 \\ 3y=63 \\ \\ \text{Divide both sides of the equation into 3:} \\ \frac{3}{3}y=\frac{63}{3} \\ \\ y=21 \end{gathered}[/tex]
Then, the solution for the system is :
[tex]\begin{gathered} x=9 \\ y=21 \end{gathered}[/tex]
Kaylee earns a profit of $9 from every bracelet and $21 from every necklace
