Linear inequality problem determining minimum CD players needed for profit.

Let’s solve this step by step.

We are told:
- Profit per DVD player = $125 → let x = number of DVD players sold
- Profit per CD player = $100 → let y = number of CD players sold
- Goal: total profit ≥ $500

So the inequality is:
125x + 100y ≥ 500

Now, we’re told the store sells only 2 DVD players, so plug in x = 2:

→ 125(2) + 100y ≥ 500
→ 250 + 100y ≥ 500

Subtract 250 from both sides:

→ 100y ≥ 250

Divide both sides by 100:

→ y ≥ 2.5

But you can’t sell half a CD player — you have to sell whole units. So if y must be at least 2.5, then the smallest whole number that works is 3.

Check: If they sell 2 DVD players and 3 CD players:

Profit = 125×2 + 100×3 = 250 + 300 = $550 → which is ≥ $500 ✔

If they sold only 2 CD players:

Profit = 250 + 200 = $450 → too low ✘

So yes, they need to sell at least 3 CD players.

Final Answer:
The store must sell at least 3 CD players.