Net Income Stereos
1. **State the problem:**
Ahnah rebuilds used stereos with variable costs of $170 per stereo and sells them for $300 each. The break-even point is 50 units per month. We need to find her net income when she sells 60 units.
2. **Formula and explanation:**
The break-even point in units is given by:
$$\text{Break-even units} = \frac{\text{Fixed Costs}}{\text{Price per unit} - \text{Variable cost per unit}}$$
At break-even, net income is zero.
3. **Find fixed costs:**
Let $F$ be fixed costs.
$$50 = \frac{F}{300 - 170} = \frac{F}{130}$$
Multiply both sides by 130:
$$F = 50 \times 130 = 6500$$
4. **Calculate net income for 60 units:**
Net income formula:
$$\text{Net Income} = (\text{Price} - \text{Variable Cost}) \times \text{Units Sold} - \text{Fixed Costs}$$
Substitute values:
$$= (300 - 170) \times 60 - 6500$$
$$= 130 \times 60 - 6500$$
$$= 7800 - 6500 = 1300$$
5. **Final answer:**
Ahnah's net income for selling 60 units is $1300.00.