A vendor at the State Fair has learned that, by pricing his deep fried bananas on a stick at $1.00, sales will reach 82 bananas per day. Raising the price to $1.75 will cause the sales to fall to 52 bananas per day. Let y be the number of bananas the vendor sells at x dollars each. Write a linear equation that models the number of bananas sold per day when the price is x dollars each.

Accepted Solution

Answer:Y=-40x+122Step-by-step explanation:helloDue to the nature of the data, it is most convenient to model this problem as a linear function.To solve this problem we must use the equation that defines a line, then start assigning the corresponding valuesy1=82bananas per dayX1=1 dolary2=52bananas per dayx2=1.75dolarline ecuationy βˆ’ y 1 = m(x βˆ’ x 1 )where [tex]m=slope=\frac{y2-y1}{x2-x1} =\frac{52-82}{1.75-1}=-40[/tex]solving:Y-82=-40(x-1)Y=-40x+40+82Y=-40x+122let's try the result!Price =1dolarY=-40(1)+122=82bananas per dayPrice=1.75dolarY=-40(1.75)+122=52bananas per day