Question

Johanna sells small cakes for $60 and large cakes for $80. She earned $1200 in sales one day. Johanna found that she could represent this situation with the equation

60x+80y=1200

where x is the number of small cakes and y is the number of large cakes.

If this equation is rewritten as a function by solving for y, what would be a reasonable domain for that function?

Answer 1

`0 \le x \le 20`

Explanation:

Given

`60x + 80y = 1200`

Required

Determine the domain

`60x + 80y = 1200`

First, solve for y

`80y = 1200 - 60x`

Divide through by 80

`(80y)/(80) = (1200)/(80) - (60x)/(80)`

`y = (1200)/(80) - (60x)/(80)`

`y = 15- 0.75x`

Given that x represents large cakes

The smallest number of cakes is 0.

To get the largest, we simply set y to 0 (to get the x intercept)

`0 = 15- 0.75x`

`-15 = - 0.75x`

Solve for x

`x = (-15)/(-0.75)`

`x = 20`

Hence, the domain is:

`0 \le x \le 20`