Question

A businesswoman has $760. She wants to buy x CDs at $80 each and y cassettes at $40 each in order to resell them at a profit. She must buy more than one CD, but not more than six CDs. She must buy at least two cassettes. Write three inequalities in x and y to represent the above information?

Answer 1

The three inequalities for the businesswoman's conditions for buying CDs and cassettes are 80x + 40y <= 760, x > 1, x <= 6, and y >= 2.

Step-by-step explanation:

The businesswoman wants to buy CDs and cassettes with the $760 she has. According to the problem, x represents the number of CDs at $80 each, and y represents the number of cassettes at $40 each. To write the inequalities based on the given conditions, we consider the following:

• She can only spend $760, so the total cost of CDs and cassettes must be less than or equal to $760. This can be written as the inequality 80x + 40y ≤ 760.
• She must buy more than one CD but not more than six, which gives us two inequalities: x > 1 and x ≤ 6.
• She must buy at least two cassettes, which we can write as y ≥ 2.

Therefore, the three inequalities representing the businesswoman's conditions are:

1. 80x + 40y ≤ 760
2. x > 1
3. x ≤ 6
4. y ≥ 2