Final answer:
To find the inequality representing monthly revenues over $6500, set up the equation based on the given information and solve for x. Option a) (50 + 5x)(120 - 4x) > 6500 is the correct inequality.
Step-by-step explanation:
To find the inequality that represents monthly revenues over $6500, we need to set up an equation based on the given information and solve for x. Let's start with the original quantity of drums sold per month at a price of $120 each: 50. For each $5 decrease in price, 4 more drums are sold. So if we decrease the price by x dollars, the number of drums sold per month would be increased by 4x.
The new quantity of drums sold would be 50 + 4x, and the new price would be $120 - 5x. The monthly revenue can be calculated by multiplying the quantity and price: (50 + 4x)(120 - 5x).
To determine the inequality, we need to set up the equation (50 + 4x)(120 - 5x) > 6500. Therefore, the correct inequality to find the prices resulting in monthly revenues over $6500 is option a) (50 + 5x)(120 - 4x) > 6500.