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
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 y photos = 2x
income for x photos = 100x
income for y cards = 5y
see what you can do with that
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
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