Company A rents copiers for a monthly charge of $240 plus 8 cents per copy. Company B rents copiers for a monthly charge of $480 pluse 4 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?
Please Help and Thank You
0.08x + 240 > 0.04x + 480.
0.08x > 480 - 240.
0.08x - 0.04x = 240.
X > 6000 Copies.
To find the number of copies above which Company A's charges are higher than Company B's charges, we need to set up an equation and solve for the number of copies.
Let's represent the number of copies as "x".
For Company A, the monthly charge is $240, and the cost per copy is 8 cents. So the total monthly charge for Company A can be expressed as:
Total charge for Company A = Monthly charge + (Cost per copy * Number of copies)
Total charge for Company A = $240 + (0.08 * x)
For Company B, the monthly charge is $480, and the cost per copy is 4 cents. So the total monthly charge for Company B can be expressed as:
Total charge for Company B = Monthly charge + (Cost per copy * Number of copies)
Total charge for Company B = $480 + (0.04 * x)
We need to find the value of "x" where Company A's charges are higher than Company B's charges. So we can set up the equation:
Total charge for Company A > Total charge for Company B
$240 + (0.08 * x) > $480 + (0.04 * x)
Now, let's solve this equation to find the value of "x":
240 + 0.08x > 480 + 0.04x
0.08x - 0.04x > 480 - 240
0.04x > 240
x > 240 / 0.04
x > 6000
Therefore, the number of copies above which Company A's charges are higher than Company B's charges is 6000.
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 that number.
Let's assume the number of copies is represented by 'x.' The total monthly charge for Company A can be calculated using the formula: Total charge = Monthly charge + (Number of copies * Cost per copy). Consequently, for Company A, the formula becomes: Total charge for A = $240 + (0.08 * x).
Similarly, for Company B, the formula would be: Total charge for B = $480 + (0.04 * x).
Now, we want to find the point at which Company A's charges become higher than Company B's. Therefore, we need to set up an inequality:
Total charge for A > Total charge for B
$240 + (0.08 * x) > $480 + (0.04 * x)
To solve this inequality, we will rearrange the terms and isolate x:
0.08 * x - 0.04 * x > $480 - $240
0.04 * x > $240
Now, divide both sides by 0.04 to solve for x:
x > $240 / 0.04
x > $6,000
Thus, for any number of copies x greater than 6,000, Company A's charges will be higher than Company B's charges.