You want to sell t-shirts for $12 a piece. It cost you $40 for supplies. Is the total profit proportional to the number of t-shirts you sell?
No, the total profit is not proportional to the number of t-shirts sold. The reason is that the cost of supplies remains constant at $40, regardless of the number of t-shirts sold. Therefore, as you sell more t-shirts, the profit will increase but not in a proportional manner.
Change the scenario in to be a proportional scenario.
To determine if the total profit is proportional to the number of t-shirts sold, we need to analyze the relationship between the two variables.
Let's denote the number of t-shirts sold as x and the total profit as y.
Given that each t-shirt is sold for $12, the revenue from selling x t-shirts can be calculated as 12x.
The cost of supplies is a fixed amount of $40, which does not change with the number of t-shirts sold.
Therefore, the total profit (y) can be expressed as:
y = 12x - 40
To check if the total profit is proportional to the number of t-shirts sold, we can observe the equation.
If the equation y = 12x - 40 satisfies the criteria for a proportional relationship, it should be in the form y = kx (where k represents a constant value).
However, since there is a constant term (-40) which does not depend on x, the relationship is not proportional.
Therefore, the total profit is not proportional to the number of t-shirts sold.
To determine if the total profit is proportional to the number of t-shirts sold, we need to analyze the relationship between the number of t-shirts sold and the profit made.
First, let's calculate the profit per t-shirt. The profit per t-shirt is the selling price minus the cost of supplies. In this case, it is $12 - $40 = -$28.
Since the profit per t-shirt is negative, it means that for each t-shirt sold, you are actually losing $28. As a result, the total profit will not be proportional to the number of t-shirts sold.
In fact, the total profit is dependent on other factors such as fixed costs (like the cost of supplies) and variable costs (like any additional expenses incurred in producing t-shirts).