Company A rents copiers for a monthly charge of $360 plus 12 cents per copy. Company B rents copiers for a monthly charge of $720 plus 6 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

we want x to satisfy:

360 + .12x > 720 + .06x
x > 6000

Great answer

To determine the number of copies above which Company A's charges are higher than Company B's, we need to set up an equation and solve for the unknown number of copies.

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.

To determine the number of copies above which Company A's charges are higher than Company B's charges, we need to find the point at which their costs are equal, and then add one to that number.

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.