Let x be the profit from the bracelets and let y be the profit from the necklaces.
We know that yesterday she sold 2 bracelets and 5 necklaces and that the profit was $155, this can be express by the equation:
[tex]2x+5y=155[/tex]Today she sold 9 bracelets and 9 necklaces, and got a profit of $306, this can be represented by the equation:
[tex]9x+9y=306[/tex]Hence we have the system of equations:
[tex]\begin{gathered} 2x+5y=155 \\ 9x+9y=306 \end{gathered}[/tex]To solve it using elimination we multiply the first equation by 9 and the second equation by -2, then we have the equivalent system:
[tex]\begin{gathered} 18x+45y=1395 \\ -18x-18y=-612 \end{gathered}[/tex]Now we add this equations and solve for y:
[tex]\begin{gathered} 18x+45y-18x-18y=1395-612 \\ 27y=783 \\ y=\frac{783}{27} \\ y=29 \end{gathered}[/tex]Once we have the value of y we plug it in one of the original equations and solve for, using the first one we have:
[tex]\begin{gathered} 2x+5(29)=155 \\ 2x+145=155 \\ 2x=155-145 \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]Therefore Naomi earns a profit of $5 for every bracelet and $29 for every necklace.