Question

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

3
2
x - 3. The profit for Store #2 is modeled by the equation g(x) = -
1
4
x + 4. On what day (x) was the profit from both stores the same?
A) 3
B) 4
C) 5
D) 6

Answer 1

Option B: On the day 4 the profit from both stores will be the same.

Step-by-step explanation:

Given that two stores were opened on the same day.

The profit from store 1 is given by

`f(x)=(3)/(2) x-3`

The profit from store 2 is given by

`g(x)=-(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,

`(3)/(2) x-3=-(1)/(4) x+4`

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

`(3)/(2) x=-(1)/(4) x+7`

Adding both sides of the equation by
`(1)/(4) x`, we get,

`(7)/(4) x=7`

Multiplying both sides of the equation by
`(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.