Question

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

Answer 1

See below

Explanation:

Stephanie's profit relationship:

• f(x) = 3.50x - 110

Bryson's Tomato Sales, using the pairs of numbers let's find the relationship.

• (10, -97.50) and (20, -55.00)

Since it is also linear relationship, we'll find a slope and y-intercept:

• m = (-55 - (-97.50))/(20 - 10) = 42.50/10 = 4.25

y-intercept is:

• -97.50 = 4.25*10 + b ⇒ b = -97.50 - 42.50 = - 140

So the function is:

• g(x) = 4.25x - 140

Comparing the functions:

• f(x) = 3.50 - 110
• g(x) = 4.25 - 140

The slope of g(x) is greater than f(x) but the y-intercept is smaller

It translates as:

• Bryson sells tomatoes at greater price: 4.25 vs 3.50 per pound
• Stephanie needs to sell 110/3.5 = 31.4 pounds of tomatoes before making any profit
• Bryson needs to sell 140/4.25 = 32.9 pounds of tomatoes before making any profit