Asked by Mujika
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? Change the scenario to be a proportional scenario.
Answers
Answered by
Mujika
Show a proportional graph and equation and compare to a non proportional graph and equation.
Proportional: y =
Non Proportional: y =
Proportional: y =
Non Proportional: y =
Answered by
GPT 3.5
In order to make the scenario proportional, we need to ensure that the profit is directly proportional to the number of t-shirts sold.
Let's assume that the total profit, P, is proportional to the number of t-shirts sold, T.
We can then write the equation for the total profit as:
P = kT,
where k is the constant of proportionality.
To determine if the total profit is proportional to the number of t-shirts sold, we can analyze the situation.
According to the given information, the cost of supplies is $40. Therefore, the profit from selling x t-shirts at $12 per t-shirt would be:
Profit = Revenue - Cost of Supplies = 12x - 40
However, since we want the scenario to be proportional, the profit should vary linearly with the number of t-shirts sold. This implies that the constant of proportionality, k, must be equal to $12.
Thus, the correct equation for the total profit is:
P = 12T.
In this proportional scenario, the total profit is indeed directly proportional to the number of t-shirts sold.
Let's assume that the total profit, P, is proportional to the number of t-shirts sold, T.
We can then write the equation for the total profit as:
P = kT,
where k is the constant of proportionality.
To determine if the total profit is proportional to the number of t-shirts sold, we can analyze the situation.
According to the given information, the cost of supplies is $40. Therefore, the profit from selling x t-shirts at $12 per t-shirt would be:
Profit = Revenue - Cost of Supplies = 12x - 40
However, since we want the scenario to be proportional, the profit should vary linearly with the number of t-shirts sold. This implies that the constant of proportionality, k, must be equal to $12.
Thus, the correct equation for the total profit is:
P = 12T.
In this proportional scenario, the total profit is indeed directly proportional to the number of t-shirts sold.
Answered by
GPT 3.5
Proportional: y = 12T
In a proportional scenario, the equation relating the total profit, P, to the number of t-shirts sold, T, is given by y = 12T. The constant of proportionality is 12, which represents the profit earned per t-shirt sold.
Graphically, this equation represents a straight line passing through the origin (0, 0) with a slope of 12. As the number of t-shirts sold increases, the total profit also increases linearly.
Non Proportional: y = 12T - 40
In a non proportional scenario, the equation relating the total profit, P, to the number of t-shirts sold, T, is given by y = 12T - 40. The additional term of -40 represents the cost of supplies ($40), which is subtracted from the revenue.
Graphically, this equation represents a straight line passing through the point (0, -40) with a slope of 12. The line does not pass through the origin, indicating that even when zero t-shirts are sold, there is still a cost incurred (-$40). This non-proportional scenario results in a shift downwards on the y-axis. As the number of t-shirts sold increases, the total profit still increases linearly, but at a reduced rate due to the constant subtraction of the cost of supplies.
Comparing the two scenarios, we can see that in the proportional scenario, the total profit increases directly proportional to the number of t-shirts sold, whereas in the non-proportional scenario, the total profit increases but is reduced by a fixed cost.
In a proportional scenario, the equation relating the total profit, P, to the number of t-shirts sold, T, is given by y = 12T. The constant of proportionality is 12, which represents the profit earned per t-shirt sold.
Graphically, this equation represents a straight line passing through the origin (0, 0) with a slope of 12. As the number of t-shirts sold increases, the total profit also increases linearly.
Non Proportional: y = 12T - 40
In a non proportional scenario, the equation relating the total profit, P, to the number of t-shirts sold, T, is given by y = 12T - 40. The additional term of -40 represents the cost of supplies ($40), which is subtracted from the revenue.
Graphically, this equation represents a straight line passing through the point (0, -40) with a slope of 12. The line does not pass through the origin, indicating that even when zero t-shirts are sold, there is still a cost incurred (-$40). This non-proportional scenario results in a shift downwards on the y-axis. As the number of t-shirts sold increases, the total profit still increases linearly, but at a reduced rate due to the constant subtraction of the cost of supplies.
Comparing the two scenarios, we can see that in the proportional scenario, the total profit increases directly proportional to the number of t-shirts sold, whereas in the non-proportional scenario, the total profit increases but is reduced by a fixed cost.
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