Question

Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $3,000 for their reception. If the

reception hall charges a $100 cleanup fee plus $37 per person, find the greatest number of people that they may invite and still stay within their budget.
Mark and Heather can invite at most people to the reception
(Round down to the nearest whole person)

Answer 1

78 persons

Explanation:

Given

`Budget = 3000`

`Clean\ up = 100`

`Rate = 37\ per\ person`

Required

Determine the maximum number of person that can be invited

Let the number of persons be p.

If the hall charges $37 for 1 person, then it will charge $37p for p persons.

So:

`Charges = 37p`

The expression becomes:

`Clean\ up + Charges = Budget`

Substitute values for Clean up, Charges and Budget

`100 + 37p = 3000`

Subtract 100 from both sides

`100 - 100 + 37p = 3000 - 100`

`37p = 3000 - 100`

`37p = 2900`

Make p the subject

`p = (2900)/(37)`

`p = 78.378`

Round down

`p = 78`

Hence, they can only invite 78 people to stay within budget