Question

Analyze both functions and describe in detail under what conditions Stephanie's profit, in dollars, would be greater than Bryson's profit. Provide evidence to support your answer.

Answer 1

The number of tomatoes must be less than 40.

Explanation:

Stephanie and Bryson both grow tomatoes to sell at farmers' markets. Stephanie grew a total of 70 pounds of tomatoes to sell. She plans to sell the tomatoes for $3.50 per pound. The equation below represents the profit in dollars, f(x), she will earn by selling x pounds of the tomatoes.

f(x) = 3.50x -110

Bryson plans to sell his tomatoes at a different farmers' market. He grew a total of 90 pounds of tomatoes.

The table below shows the profit, in dollars, he will earn by selling different numbers of pounds of

tomatoes.

Bryson's Tomato Sales

-97.50 -55.00 -12.50 30,00

Profit (dollars)

Pounds of

Tomatoes Sold

10

20

30

40

Solution:

For Stephanie, let x represent the number tomatoes sold and f(x) represent the profit in dollars. The profit is given by:

f(x) = 3.5x - 110

For Bryson, let x represent the number tomatoes sold and y represent the profit in dollars. From the table, the profit can be represented by the points (10, -97.5) and (40, 30). The profit can be gotten using the formula:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-(-97.5)=(30-(-97.5))/(40-10) (x-10)\\\\y+ 97.5=4.25(x-10)\\\\y+97.5=4.25x-42.5\\\\y=4.25x-140`

Stephanie profit > Bryson profit

3.5x - 110 > 4.25x - 140

3.5x - 4.25x > -140 + 110

-0.75x > -30

x < 40