1. Marissa 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. Marissa can sell up to 8 framed photographs and 40 greeting cards each week, but this week, she only has $200 to spend on materials. Marissa hopes to earn a profit of at lest $400 this week after paying for her materials.

Question

1. Marissa 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. Marissa can sell up to 8 framed photographs and 40 greeting cards each week, but this week, she only has $200 to spend on materials. Marissa hopes to earn a profit of at lest $400 this week after paying for her materials.

Let x = the number of framed photographs.
Let y = the number of greeting cards.
Two of the inequalities that model this situation are and .
1. Marissa 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. Marissa can sell up to 8 framed photographs and 40 greeting cards each week, but this week, she only has $200 to spend on materials. Marissa hopes to earn a profit of at lest $400 this week after paying for her materials.
Let x = the number of framed photographs.
Let y = the number of greeting cards.
Two of the inequalities that model this situation are x<=8 and y<=40

Write two more inequalities to complete the system of inequalities modeling this situation

Answer 1

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Answer 2

. Explain your inequalities and explain why and are also inequalities for this system

Answer 3

To complete the system of inequalities, we need to consider the constraints of the maximum number of framed photographs and greeting cards Marissa can sell, as well as her budget for materials and desired profit.

Let's write the remaining two inequalities:

1. Budget constraint: The cost of materials for framed photographs and greeting cards must not exceed Marissa's budget of $200.
The cost of materials for framed photographs can be calculated as $30 per framed photograph multiplied by the number of framed photographs: 30x
The cost of materials for greeting cards can be calculated as $2 per greeting card multiplied by the number of greeting cards: 2y
Therefore, the inequality representing the budget constraint is:
30x + 2y ≤ 200

2. Profit constraint: Marissa wants to earn a profit of at least $400 after paying for her materials.
The profit from selling framed photographs can be calculated as the selling price ($100) minus the cost of materials ($30): 100x - 30x = 70x
The profit from selling greeting cards can be calculated as the selling price ($5) minus the cost of materials ($2): 5y - 2y = 3y
Therefore, the inequality representing the profit constraint is:
70x + 3y ≥ 400

The complete system of inequalities modeling this situation is:
x ≤ 8
y ≤ 40
30x + 2y ≤ 200
70x + 3y ≥ 400