Question

1. serafina can choose between two dining halls for a banquet. hall a charges $200 plus $4 per person. hall b charges $150 plus $5 per person. how many people would have to attend for the charges to be the same? (7-7)

dining hall	number of people
a	$200	$240	$280
b	$150	$200	$250

a 30
b 40
c 50
d 60

Explanation:

Step1: Define variables and cost functions

Let \( x \) be the number of people. The cost for Hall A, \( C_A \), is \( C_A = 200 + 4x \) (a fixed cost of $200 plus $4 per person). The cost for Hall B, \( C_B \), is \( C_B = 150 + 5x \) (a fixed cost of $150 plus $5 per person).

Step2: Set costs equal and solve for \( x \)

We want to find \( x \) when \( C_A = C_B \). So:
\[
200 + 4x = 150 + 5x
\]
Subtract \( 4x \) from both sides:
\[
200 = 150 + x
\]
Subtract 150 from both sides:
\[
x = 200 - 150 = 50
\]

Answer:

C. 50