The equation C(x) = 100x + 100,000/x models the average cost (C(x)) for a manufacturer to produce x bicycles. How many bicycles must be produced to bring the average cost per bicycle to $125?
125(x)= 100x + 100,000/x
would i then divide both sides by the 125? not sure what comes next
To find the number of bicycles that must be produced to bring the average cost per bicycle to $125, you need to solve the equation:
125x = 100x + 100,000/x
To begin solving this equation, you can start by getting rid of the fraction by multiplying both sides of the equation by x:
125x * x = (100x + 100,000/x) * x
This simplifies to:
125x^2 = 100x^2 + 100,000
Next, rearrange the equation by subtracting 100x^2 from both sides:
125x^2 - 100x^2 = 100,000
Simplifying further:
25x^2 = 100,000
Now, divide both sides of the equation by 25 to isolate the variable x:
25x^2/25 = 100,000/25
This simplifies to:
x^2 = 4,000
To solve for x, take the square root of both sides:
√(x^2) = √4,000
This gives you:
x = ± √4,000
However, since you're talking about the number of bicycles produced, it doesn't make sense to have a negative number of bicycles. Therefore, you take the positive square root:
x = √4,000
Calculating the square root:
x ≈ 63.25
Rounding to a whole number, you would need to produce at least 64 bicycles to bring the average cost per bicycle to $125.