Question

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.

Answer 1

Y=-40x+122

Explanation:

hello

Due 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 values

y1=82bananas per day

X1=1 dolar

y2=52bananas per day

x2=1.75dolar

line ecuation

y − y 1 = m(x − x 1 )

where

`m=slope=(y2-y1)/(x2-x1) =(52-82)/(1.75-1)=-40`

solving:

Y-82=-40(x-1)

Y=-40x+40+82

Y=-40x+122

let's try the result!

Price =1dolar

Y=-40(1)+122=82bananas per day

Price=1.75dolar

Y=-40(1.75)+122=52bananas per day