Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Rita is making greeting cards, which she will sell by the box at an arts fair. She paid $24 for a booth at the fair, and the materials for each box of cards cost $3. She will sell the cards for $11 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How much will the sales and expenditures be? How many cards will that take?

we need to find the number n of sold boxes, so that the income (sales) and costs (expenditures) are equal. this is called the break even point. any more boxes sold will then result in a profit, actually gaining money. and if she cannot reach that number of sold boxes, then she will make a loss.

so,

n×11 = n×3 + 24

n×8 = 24

n = 3

it will take 3 sold boxes of cards to break even.

at that point she will have spent $24 + 3×$3 = $33, and her sales will be 3×$11 = $33.