we want x to satisfy:
360 + .12x > 720 + .06x
x > 6000
360 + .12x > 720 + .06x
x > 6000
Let's suppose the unknown number of copies is represented by x.
For Company A, the monthly charge is $360 plus 12 cents per copy, which can be represented by the equation:
A(x) = 360 + 0.12x
For Company B, the monthly charge is $720 plus 6 cents per copy, which can be represented by the equation:
B(x) = 720 + 0.06x
We want to find the point at which A(x) is greater than B(x), so we set up the following inequality:
A(x) > B(x)
Substituting the equations, we get:
360 + 0.12x > 720 + 0.06x
Simplifying the equation, we get:
0.12x - 0.06x > 720 - 360
0.06x > 360
x > 360 / 0.06
x > 6000
Therefore, Company A's charges are higher when the number of copies is above 6000.
Let's represent the number of copies by "x."
For Company A, the total cost is given by the equation: 360 + 0.12x.
For Company B, the total cost is given by the equation: 720 + 0.06x.
To find the point at which their costs are equal, we need to set the two equations equal to each other and solve for x:
360 + 0.12x = 720 + 0.06x
Subtracting 0.06x from both sides, we get:
0.06x = 720 - 360
Combining like terms, we have:
0.06x = 360
Now, divide both sides by 0.06 to solve for x:
x = 360 / 0.06
Performing the division, we find:
x = 6000
So, when the number of copies reaches 6000, the costs for Company A and Company B are equal.
To find the number of copies above which Company A's charges are higher, we add 1 to 6000:
6000 + 1 = 6001
Therefore, the number of copies above which Company A's charges are higher than Company B's charges is 6001 copies.