The cost (in thousands of dollars) of the production of scooters can be representedby x^2 - 10x + 27, where x is the number of scooters produced. What is the minimum number of scooters that can be produced for $6 thousand?
X=3 or 7, so the answer is 3
To find the minimum number of scooters that can be produced for $6 thousand, we need to set up an equation and solve for x.
The equation for the cost of production is given as:
Cost = x^2 - 10x + 27
We want to find the minimum number of scooters produced for $6 thousand, so we set up the equation as:
6 = x^2 - 10x + 27
Rearranging the equation to put it in quadratic form:
x^2 - 10x + 27 - 6 = 0
x^2 - 10x + 21 = 0
Now we can solve this equation by factoring or using the quadratic formula.
Factoring the quadratic equation:
(x - 3)(x - 7) = 0
Setting each factor to zero:
x - 3 = 0 or x - 7 = 0
This gives us two possible solutions:
x = 3 or x = 7
Since the number of scooters produced cannot be negative, the minimum number of scooters that can be produced for $6 thousand is 7.
To find the minimum number of scooters that can be produced for $6 thousand, we need to set the cost equation equal to $6 thousand (which is equivalent to $6000) and solve for the number of scooters, represented by x.
The cost equation, x^2 - 10x + 27, represents the cost of production in thousands of dollars. So, we can rewrite the equation as x^2 - 10x + 27 = 6.
Next, we need to solve this equation to find the value of x. To do this, we can rearrange the equation to put it in standard quadratic form:
x^2 - 10x + 27 - 6 = 0
x^2 - 10x + 21 = 0
Now, we can use factoring, completing the square, or the quadratic formula to solve for x. Let's use factoring to solve the equation:
(x - 3)(x - 7) = 0
Setting each factor equal to zero:
x - 3 = 0 or x - 7 = 0
Solving for x:
x = 3 or x = 7
Therefore, the equation has two solutions: x = 3 or x = 7. This means that the minimum number of scooters that can be produced for $6 thousand is either 3 scooters or 7 scooters.