Question

Naomi is selling her handmade jewelry online. Yesterday, she sold 2 bracelets and 5 necklaces, for a profit of $155. Today, she made a profit of $306 by selling 9 bracelets and 9 necklaces. How much profit does Naomi earn from each piece?

Answer 1

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:

`2x+5y=155`

Today she sold 9 bracelets and 9 necklaces, and got a profit of $306, this can be represented by the equation:

`9x+9y=306`

Hence we have the system of equations:

`\begin{gathered} 2x+5y=155 \\ 9x+9y=306 \end{gathered}`

To solve it using elimination we multiply the first equation by 9 and the second equation by -2, then we have the equivalent system:

`\begin{gathered} 18x+45y=1395 \\ -18x-18y=-612 \end{gathered}`

Now we add this equations and solve for y:

`\begin{gathered} 18x+45y-18x-18y=1395-612 \\ 27y=783 \\ y=(783)/(27) \\ y=29 \end{gathered}`

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:

`\begin{gathered} 2x+5(29)=155 \\ 2x+145=155 \\ 2x=155-145 \\ 2x=10 \\ x=(10)/(2) \\ x=5 \end{gathered}`

Therefore Naomi earns a profit of $5 for every bracelet and $29 for every necklace.