Question

A mail distribution center processes as many as 175,000 pieces of mail each day. The mail is sent via ground and air. Each land carrier 1250 pieces per load. The loading equipment is able to handle as many as 200 loads per day. Let x be the number of loads by land carriers and y the number of loads by air carriers. Which system of inequalities represents this situation? A) 1250x+1500y<=175,000 x+y<=200 B) 1500x+1250y=>175,000 x+y=>200 C) 1500x+1250<=175,000 x+y<=200 D) 1250x+1500y=>175,000 x+y=>200

Answer 1

The correct system of inequalities representing the mail distribution scenario is A) 1250x+1500y<=175,000 x+y<=200, with x being the number of land carrier loads and y the number of air carrier loads. This system accounts for both the maximum number of pieces processed and the total number of loads the equipment can handle daily.

Step-by-step explanation:

The question concerns a mail distribution center's capacity to process mail via ground (land carriers) and air. To express this scenario mathematically, we create a system of inequalities with x representing the number of land carrier loads and y representing the number of air carrier loads.
The land carriers transport 1250 pieces per load (1250x), and the total processed mail should not exceed 175,000 pieces per day. In addition, the loading equipment can handle no more than 200 loads per day, whether by land or air (x + y).

Given these constraints, the appropriate system of inequalities is:
1250x + 1500y ≤ 175,000
x + y ≤ 200
This matches option A. There is no information regarding the capacity per load for air carriers, but since the other inequalities and values given do not match the scenario described, we can deduce that there is a typo and it should be '1250' instead of '1500' for air carriers.

Answer 2

The total number of mails that is processed by the mail distribution center cannot go beyond 175,000 (because this is the maximum number of mails). Therefore, the first equation that can be generated from the given scenario is,
1250x + 1500y ≤ 175000
Also, since the maximum number of loads per day can only be 200, the second equation would be,
x + y ≤ 200
Therefore, the answer to this item is letter A.