Michele is a photographer. She sells framed photographs for $100 each and greeting cards for $5 each. The materials for each framed photograph cost $30, and the materials for each greeting card cost $2. Michele can sell up to 8 framed photographs and 40 greeting cards each week, but this week she has only $200 to spend on materials. Michele hopes to earn a profit of at least $400 this week after paying for materials. Let x = the number of framed photographs and y= the number of greeting cards Michele will make and sell this week.

Write a number on each blank line in the following statement to make it true.
Two of the inequalities that model this situation are
x< ___________ and y < ___________
Write two more inequalities to complete the systems of inequalities modeling the situation.

cost for x photos = 30x

cost for y photos = 2x

income for x photos = 100x
income for y cards = 5y

see what you can do with that

Two of the inequalities that model this situation are:

x < 8
y < 40

To complete the system of inequalities, two more inequalities can be added based on the given information:

30x + 2y ≤ 200 (representing the limit of $200 to spend on materials)
(100x + 5y) - (30x + 2y) ≥ 400 (representing the desired profit of at least $400 after paying for materials)

Therefore, the complete system of inequalities modeling the situation is:

x < 8
y < 40
30x + 2y ≤ 200
(100x + 5y) - (30x + 2y) ≥ 400

Two of the inequalities that model this situation are:

x < 8 (since Michele can sell up to 8 framed photographs each week)
y < 40 (since Michele can sell up to 40 greeting cards each week)

To complete the systems of inequalities, we need to consider the constraints on the budget and the profit. Let's introduce two more inequalities:

1) Constraints on the budget:
The cost of materials for each framed photograph is $30, and the cost of materials for each greeting card is $2. The total budget for materials is $200. So, the inequality for the budget constraint can be written as:
30x + 2y ≤ 200

2) Profit constraint:
Michele hopes to earn a profit of at least $400. The profit for each framed photograph is $100 - $30 = $70, and the profit for each greeting card is $5 - $2 = $3. Therefore, the profit equation can be expressed as:
70x + 3y ≥ 400

Adding these two additional inequalities completes the systems of inequalities modeling the situation:
x < 8
y < 40
30x + 2y ≤ 200
70x + 3y ≥ 400