Final answer:
The total profit Sarah makes can be calculated using the linear equation P = 30x + 50y, where x represents the number of small purses and y represents the number of big purses sold.
Step-by-step explanation:
The total profit Sarah makes from selling small and big purses can be calculated by creating a linear equation based on the number of small purses (x) and big purses (y) she sells. Since Sarah makes $30 for each small purse and $50 for each big purse, the total profit (P) can be expressed as: P = 30x + 50y.
For example, if Sarah sells 3 small purses and 2 big purses, her total profit would be calculated as follows:
P = (30 × 3) + (50 × 2) = 90 + 100 = $190.
This formula allows Sarah to easily determine her total profits by simply substituting the values of x and y with the number of small and big purses sold, respectively.