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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 :

MRROYALGO

Answer:

[tex]0 \le x \le 20[/tex]

Step-by-step explanation:

Given

[tex]60x + 80y = 1200[/tex]

Required

Determine the domain

[tex]60x + 80y = 1200[/tex]

First, solve for y

[tex]80y = 1200 - 60x[/tex]

Divide through by 80

[tex]\frac{80y}{80} = \frac{1200}{80} - \frac{60x}{80}[/tex]

[tex]y = \frac{1200}{80} - \frac{60x}{80}[/tex]

[tex]y = 15- 0.75x[/tex]

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)

[tex]0 = 15- 0.75x[/tex]

[tex]-15 = - 0.75x[/tex]

Solve for x

[tex]x = \frac{-15}{-0.75}[/tex]

[tex]x = 20[/tex]

Hence, the domain is:

[tex]0 \le x \le 20[/tex]

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