Answer:
The number of tomatoes must be less than 40.
Step-by-step 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:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-97.5)=\frac{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[/tex]
Stephanie profit > Bryson profit
3.5x - 110 > 4.25x - 140
3.5x - 4.25x > -140 + 110
-0.75x > -30
x < 40
