Jan is a photographer. She earns $42.50 for each picture she sells. It costs Jan $850.00 per month to maintain her photography lab.
Write an equation that represents the relationship between Jan's monthly profit (P) and the number of pictures (x) she sells.
What does the x-intercept of the graph of the equation you found represent to Jan?
P = 42 x - 850
x intercept is when P = 0, break even
To write an equation that represents the relationship between Jan's monthly profit (P) and the number of pictures (x) she sells, we need to consider the revenue (income) and the expenses.
The revenue Jan earns from selling pictures is calculated by multiplying the number of pictures sold (x) by the income earned from each picture, which is $42.50. Therefore, the revenue is given by: Revenue = (Number of pictures sold) * (Income per picture) = x * 42.50.
Jan's expenses for maintaining her photography lab are a fixed cost of $850 per month.
To calculate the monthly profit (P), we subtract the expenses from the revenue: Monthly Profit = Revenue - Expenses = (x * 42.50) - 850.
Now we have the equation that represents the relationship between Jan's monthly profit (P) and the number of pictures (x) she sells:
P = (x * 42.50) - 850.
The x-intercept of the graph of this equation represents a point where the monthly profit (P) is equal to zero. In other words, it's the value of x where Jan's revenue from selling pictures is equal to her expenses for maintaining the lab, resulting in no profit. Therefore, the x-intercept represents the number of pictures Jan needs to sell to break even - where she covers her expenses but doesn't make any profit.