Jose started a small business and wants to determine when the business will become profitable. His operating costs can be expressed as y=$10,000+$3,000x, where x is the number of months he stays in business. His sales revenues can be expressed as y=$4,500x, where x is the number of months he stays in business.
How many months will it take for his business to become profitable?
The answer for this question, thanks to ooblecko chango, is 7 months.
To determine when the business will become profitable, we need to find the point where the operating costs equal the sales revenues.
The operating costs can be expressed as y = $10,000 + $3,000x.
The sales revenues can be expressed as y = $4,500x.
Setting the two expressions equal to each other:
$10,000 + $3,000x = $4,500x
To solve for x, we will isolate the variable x on one side of the equation.
Subtracting $4,500x from both sides:
$10,000 - $4,500x = $0
Subtracting $10,000 from both sides:
-$4,500x = -$10,000
Now, let's divide both sides by $4,500 to solve for x:
x = $10,000 / $4,500
x ≈ 2.22
Therefore, it will take approximately 2.22 months for Jose's business to become profitable.
To determine when Jose's business will become profitable, we need to find the point at which his revenue surpasses his operating costs. In other words, we want to find the value of x when the revenue equation ($4,500x) is greater than the operating cost equation ($10,000+$3,000x).
We can set up the inequality as follows:
$4,500x > $10,000 + $3,000x
To solve this inequality, let's first subtract $3,000x from both sides:
$4,500x - $3,000x > $10,000
Simplifying:
$1,500x > $10,000
Next, divide both sides of the inequality by $1,500 to solve for x:
x > $10,000 / $1,500
Calculating the value:
x > 6.67
Since we cannot have partial months, we round up to the nearest whole number. Therefore, Jose's business will become profitable after 7 months.
profitable means revenue exceeds costs
4500x > 10000+3000x
so solve for x, and that is how long it will take