Final answer:
To find the number of pounds for which the shipping charges are equal, set the two shipping company equations equal to each other and solve for x.
Step-by-step explanation:
The shipping charges for Company A can be represented by the equation y = 0.75x + 8, where x is the weight in pounds and y is the total shipping cost. The shipping charges for Company B can be represented by the equation y = cx + 12, where c is the cost per pound.
To find the number of pounds for which the shipping charges are equal, we can set the two equations equal to each other and solve for x:
0.75x + 8 = cx + 12 (Substitute the equations)
-0.75x + cx = 12 - 8 (Rearrange terms)
(c - 0.75)x = 4 (Combine like terms)
x = 4 / (c - 0.75) (Divide by (c - 0.75))
Therefore, the number of pounds for which the shipping charges are equal is 4 / (c - 0.75).