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?

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.