Question

Joes Catering Company charges a $45 set-up fee plus $12.50 per person. Jimmys catering company charges a $75 set up fee plus $7.50 per person. Which inequality could be used to determine x, the number of people for which Joes Catering Company would be less expensive than Jimmys catering company?

a) 45 + 12.50x < 75 + 7.50x
b) 45 + 12.50x > 75 + 7.50x
c) 45 + 12.50x >75 + 7.50x
d) 45 + 12.50x > 75 + 7.50x

Answer 1

The inequality that could be used to determine the number of people for which Joes Catering Company would be less expensive than Jimmys Catering Company is a) 45 + 12.50x < 75 + 7.50x.

Step-by-step explanation:

The inequality that could be used to determine the number of people for which Joes Catering Company would be less expensive than Jimmys Catering Company is a) 45 + 12.50x < 75 + 7.50x.

To understand why, we need to compare the costs of the two catering companies. Joes Catering charges a set-up fee of $45 plus $12.50 per person, while Jimmys Catering charges a set-up fee of $75 plus $7.50 per person.

To determine which is less expensive, we need to compare the costs when x represents the number of people. The cost for Joes Catering can be represented as 45 + 12.50x, and the cost for Jimmys Catering can be represented as 75 + 7.50x. We can see that Joes Catering will be less expensive when its cost is less than Jimmys Catering, which is why option a) is the correct inequality.