Answer:
At 16 people company B will be the cheaper option
Explanation:
Assume that the number of people is x
∵ Company A charges $32 per person to host a banquet
∵ The number of people is x
∴ The cost of company A = 32x
∵ Company B charges an initial fee of $30 and charges $30 per person
∵ The number of people is x
∴ The cost of company B = 30x + 30
∵ Company B be is the cheaper option
→ That means the cost of company B < The cost of company A
∴ 30x + 30 < 32x
→ Subtract 30x from both sides
∵ 30x - 30x + 30 < 32x - 30x
∴ 30 < 2x
→ Divide both sides by 2
∴ 15 < x
→ 15 smaller than x means x is greater than 15
∴ x > 15
→ To make company B cheaper, the number of people should be > 15
∵ The first integer greater than 15 is 16
∴ At 16 people company B will be the cheaper option