Liam's is planning a banquet for his parents anniversary with a budget of $3,375 at a hotel ballroom. The venue can hold no more than 125 guests. The cost per adult is $45 and the cost per child is $15. What is the possible number of guests that could attend the banquet within the budget?

With 3375 being there budget they can have 125 people their maximum amount by have 50 adults and 75 kids

50 adults could attend, along with 75 children, for $3,375.

Step-by-step explanation:

Let a represent the number of adult attendees and c the number of children.

Then a + c = 125, and

($45/adult) a + ($15/child) c = $3,375.

Let's solve this using the elimination method (adding and subtracting):

Multiplying the first equation by - 45 results in - 45a - 45c = - 5625:

Then we have

45a + 15c = 3375

-45a - 45c = - 5625

and combining these two equations results in the single equation

-30c = - 2250. This is easily solved for c: c = 75.

Since we already have a formula for a, we can find a given that c = 75:

a = 125 - 75 = 50

50 adults could attend, along with 75 children, for $3,375.