Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Zoe is making greeting cards, which she will sell by the box at an arts fair. She paid $22 for a booth at the fair, and the materials for each box of cards cost $4. She will sell the cards for $15 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take? How much will the sales and expenditures be?

Answer 1

Let x be the number of box cards

Expenditures: $22 plus $4 times x

`E=22+4x`

Sales: $15 times x

`S=15x`

At some point, she will sell enough cards so that her sales of her cover her expenditures of her: Equal E and S

`E=S`

Substitute the values of E and S:

`22+4x=15x`

Solve x:

`\begin{gathered} 22+4x-4x=15x-4x \\ 22=11x \\ (22)/(11)=(11)/(11)x \\ 2=x \\ \\ \\ x=2 \end{gathered}`

Use the value of x to find the sales and expenditures:

`\begin{gathered} S=15x \\ S=15(2) \\ S=30 \\ \\ E=22+4x \\ E=22+4(2) \\ E=22+8 \\ E=30 \end{gathered}`

Then, It takes to Zoe sell 2 box cards to cover the expenditures, the sales need to be $30 to cover the expenditures