Company A charges $32 per person to host a banquet. Company B charges an initial fee of $30 and charges $30 per person. At what number of people will Company B be the cheaper option?

At 16 people company B will be the cheaper option

Step-by-step 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