Question

Two stores opened on the same day. The profit for Store #1 is modeled by the equation f(x) =

Answer 1

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

$f(x)=\frac{3}{2} x-3$

The profit from store 2 is given by

$g(x)=-\frac{1}{4} x+4$

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,

$\frac{3}{2} x-3=-\frac{1}{4} x+4$

Adding both sides of the equation by 3, we get,

$\frac{3}{2} x=-\frac{1}{4} x+7$

Adding both sides of the equation by $\frac{1}{4} x$, we get,

$\frac{7}{4} x=7$

Multiplying both sides of the equation by $\frac{4}{7}$, we get,

$x=4$

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.