Option B: On the day 4 the profit from both stores will be the same.
Explanation:
Given that two stores were opened on the same day.
The profit from store 1 is given by
[tex]f(x)=\frac{3}{2} x-3[/tex]
The profit from store 2 is given by
[tex]g(x)=-\frac{1}{4} x+4[/tex]
We need to determine the day on which the profit from both the stores will be same.
Let us equate the two equations.
Thus, we have,
[tex]\frac{3}{2} x-3=-\frac{1}{4} x+4[/tex]
Adding both sides of the equation by 3, we get,
[tex]\frac{3}{2} x=-\frac{1}{4} x+7[/tex]
Adding both sides of the equation by [tex]\frac{1}{4} x[/tex], we get,
[tex]\frac{7}{4} x=7[/tex]
Multiplying both sides of the equation by [tex]\frac{4}{7}[/tex], we get,
[tex]x=4[/tex]
Thus, the value of x is 4.
Hence, On the day 4 the profit from both stores will be the same.
Therefore, Option B is the correct answer.
