Mark and heather starr are celebrating their 25th anniversary by having a reception at a local reception hall. they have budgeted $2,000 for their reception. if the reception hall charges a $90 clean-up fee plus $34 per person, find the greatest number of people that they may invite and still stay within their budget.

The maximum number of people that can be invited is 56.

Based on the information given in the question, the equation to solve the question will be:

90 + 34p = 2000

where p = number of people

90 + 34p = 2000

Collect like terms

34p = 2000 - 90

34p = 1910

Divide both side by 34

34p/34 = 1910/34

p = 56

Therefore, the number of people that can be invited will be 56

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If p represents the number of people attending, then the charges will be

... 90 +34p

and Mark and Heather want that value to be less than or equal to 2000.

... 90 +34p ≤ 2000

... 34p ≤ 1910

... p ≤ 56.2

The greatest number of people attending can be 56.

If Mark and Heather come without invitations, the greatest number they can invite is 54.