Final answer:
To find the total number of guests at the banquet, we can use algebraic equations. By setting up equations for the number of guests who ordered each type of food and solving them, we can determine that a total of 132 guests attended the banquet.
Step-by-step explanation:
To solve this problem, we can use algebraic equations. Let's represent the number of guests who ordered chicken as 'C', the number who ordered steak as 'S', and the number who ordered seafood as 'SE'.
From the given information, we can set up the following equations:
- C = 43
- S = C + 12
- SE = C - 9
We want to find the total number of guests, so we need to find the value of C first. We can substitute the value of C in the other equations to solve for S and SE. Once we have the values of S and SE, we can find the total number of guests by adding them up.
Let's substitute the value of C in the equations:
- S = 43 + 12 = 55
- SE = 43 - 9 = 34
Finally, we can find the total number of guests by adding C, S, and SE:
Total number of guests = C + S + SE = 43 + 55 + 34 = 132