Question

William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. If the reception hall charges a $80 cleanup fee plus $34 per​ person, find the greatest number of people that they may invite and still stay within their budget.

Answer 1

The greatest number of people that they may invite and still stay within their budget is 130 people.

The standard form of a linear equation is given by:

y = mx + b

Where y is a dependent variable, x is an independent variable, m is the slope of the line (the rate of change), b is the y intercept (that is the initial value of y).

Let y represent the budget for x number of people.

Since the reception hall charges a $80 cleanup fee plus $34 per​ person, hence this can be represented by the function:

y = 34x + 80

They have budgeted $4,500 for their reception. Therefore the greatest number of people can be found from:

4500 = 34x + 80

34x = 4420

x = 130 people

Therefore the greatest number of people that they may invite and still stay within their budget is 130 people.

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