Inequalitites and Applications

Question

We are planning a reception for our daughter. The hall that we are renting charges a $60 cleanup fee. In addition to the cleanup fee, they charge $40 per guest for food and drinks.

If we have $3,550.00 available, what is the maximum number of guests we can invite without going over our budget?

The maximum number of guests is :

Answer 1

60 + 40x ≤ 3550 => x≤87

Answer 2

In more detail:

60 + 40x =< 3550

Subtract 60 from both sides (to isolate the 40x term):

40x =< 3490

Divide both sides by the coefficient of x:

40x/40 = x =< 3490/40 = 87.25

Since you can't have one quarter of a person, the maximum number of guests is 87.