Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $2,500 for their reception. If the reception hall charges a $60 cleanup fee plus $39 per person, find the greatest number of people that they may invite and still stay within their budget.

62 persons

Step-by-step explanation:

Step one:

given data

total budget=$2500

we are told that the hall charges $60 for cleanup, the amount is a fix charge

and per person is $39

let the number of persons be x

The model for the situation is described by y=mx+c

Step two:

2500=39x+60

solve for x

2500-60=39x

2440=39x

divide both sides by 39 we have

x=2440/39

x=62.56

The greatest number of people that they may invite and still stay within their budget.  is 62

  Slope = 0.143/2.000 = 0.071  a-intercept = 0/1 = 0.00000  h-intercept = 0/-14 = -0.00000Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     a-(1/2*h*(20+8))=0 

Step by step solution :
Step  1  : 1 Simplify — 2 Equation at the end of step  1  : 1 a - ((— • h) • 28) = 0 2
Step  2  :Equation at the end of step  2  : a - 14h = 0
Step  3  :Equation of a Straight Line

 3.1     Solve   a-14h  = 0 

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). 

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  a-14h  = 0 and calculate its properties

Graph of a Straight Line : Calculate the Y-Intercept :

Notice that when a = 0 the value of h is 0/-14 so this line "cuts" the h axis at h=-0.00000

  h-intercept = 0/-14 = -0.00000 Calculate the X-Intercept :

When h = 0 the value of a is 0/1 Our line therefore "cuts" the a axis at a= 0.00000

  a-intercept = 0/1 = 0.00000 Calculate the Slope :

Slope is defined as the change in h divided by the change in a. We note that for a=0, the value of h is 0.000 and for a=2.000, the value of h is 0.143. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 0.143 - 0.000 = 0.143 in h. (The change in h is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

  Slope = 0.143/2.000 = 0.071 Geometric figure: Straight Line 
 
Slope = 0.143/2.000 = 0.071  a-intercept = 0/1 = 0.00000  h-intercept = 0/-14 = -0.00000