Question

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

Lillian is making greeting cards, which she will sell by the box at an arts fair. She paid $20 for a booth at the fair, and the materials for each box of cards cost $2. She will sell the cards for $6 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?
Lilian’s expenditures will be $____ if she sells ____ boxes of cards of cards

Answer 1

Lilian's expenditures will be $0 if she sells 5 boxes of cards of cards

Explanation:

20€= euros she paid for the booth

€2= euros for a box

€6= euros she will have for 1 box sold

?= sales

?= expenditures

?= cards sold to have sales=x

x: 5

expenditures: 20+2x=20+2×5=20+10=30

sales: 6x-(expenditures)= 6x-(20+2x)= 6×5-(20+2×5)= 30- (20+10)= 0

x:6

expenditures: 20+2x= 20+2×6=20+12=32

sales: 6x-(20+2x)= 6×6-(20+2×6)= 36- (20+12)=36-32=4

Answer 2

How much will the sales and expenditures be? $30

How many cards will that take? 5 boxes

Lilian’s expenditures will be $__30__ if she sells __5__ boxes of cards of cards.

Explanation:

We need an equation of costs and an equation of revenue (income).

Let x = number of boxes.

Let c = costs.

Let r = revenue.

Costs:

$20 fixed cost for the booth

$2 per box, or 2x for x boxes

cost equation: c = 2x + 20

Revenue:

$6 per box, or 6x for x boxes.

revenue equation: r = 6x

We want to find the number of boxes, x, for which the cost and the revenue are equal, r = c.

c = 2x + 20

r = 6x

r = c

6x = 2x + 20

4x = 20

x = 5

With 5 boxes, the costs are:

c = 2x + 20 = 2(5) + 20 = 30

Answer:

How much will the sales and expenditures be? $30

How many cards will that take? 5 boxes

Lilian’s expenditures will be $__30__ if she sells __5__ boxes of cards of cards.