Question

Write a system of equations to describe the

situation below, solve using any method, and
fill in the blanks.

Jessica is making greeting cards, which she
will sell by the box at an arts fair. She paid
$42 for a booth at the fair, and the materials
for each box of cards cost $6. She will sell
the cards for $12 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?
If Jessica sells
boxes of cards of
cards, she will break even, with sales and
expenditures of $

Answer 1

Explanation:

To solve the problem, we can set up a system of equations to represent Jessica's sales and expenditures. Let x be the number of boxes of cards she sells.

Then, the total cost of her materials will be 6x dollars, and her total revenue from sales will be 12x dollars. Her expenditures will include the cost of materials and the booth fee, which is 42 dollars. Therefore, we can write the following system of equations:

6x + 42 = 12x

Simplifying and solving for x, we get:

6x = 42

x = 7

Therefore, Jessica will need to sell 7 boxes of cards in order to break even. The sales from these 7 boxes will be:

7 boxes * 12 dollars/box = 84 dollars

The expenditures will include the cost of materials and the booth fee, which is:

6 dollars/box * 7 boxes + 42 dollars = 84 dollars

So, the sales and expenditures will both be 84 dollars if Jessica sells 7 boxes of cards.