Question

Skill plansTX StandaScienceRecommendationsA Math49 Language artsSocial studiesAlgebra 1> 0.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! GotWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Kaylee is selling her handmade jewelry online. Yesterday, she sold 9 bracelets and 3necklaces, for a profit of $144. Today, she made a profit of $279 by selling 10 bracelets and 9necklaces. How much profit does Kaylee earn from each piece?Kaylee earns a profit of $|| from every bracelet and $from every necklace.Submit

Answer 1

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:

`9x+3y=144`

Today, she made a profit of $279 by selling 10 bracelets and 9 necklaces:

`10x+9y=279`

System of equations:

`\begin{gathered} 9x+3y=144 \\ 10x+9y=279 \end{gathered}`

To solve by elimination:

1. Multiply the first equation by -3:

`\begin{gathered} -3(9x+3y=144 \\ \\ -27x-9y=-432 \end{gathered}`

2. Add equation you get in step 1 and the second equation in the system:

`-17x=-153`

3. Use the equation you get in step 2 to solve x:

`\begin{gathered} \text{Divide both sides of the equation into -17} \\ \\ (-17)/(-17)x=(-153)/(-17) \\ \\ x=9 \end{gathered}`

4. Use the value of x to solve y:

`\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:} \\ (3)/(3)y=(63)/(3) \\ \\ y=21 \end{gathered}`

Then, the solution for the system is :

`\begin{gathered} x=9 \\ y=21 \end{gathered}`

Kaylee earns a profit of $9 from every bracelet and $21 from every necklace