Chapter ISG, Problem 4.5STP

a.

To determine

To form an equation for the given statement

Answer to Problem 4.5STP

The equation of line is $y=13x+69$

Explanation of Solution

Given information:

Serving 45 people the bill is $654

Serving 68 people the bill is $953

Formula Used:

The equation of line in point slope form is,

  $y-y1=m(x-x1)$

Equation of line in slope intercept form is,

  $y=mx+c$

Slope is,

  $m=\frac{y2-y1}{x2-x1}$

Calculation:

The given two points are (45, 654) and (68, 953)

For slope substituting the values in the formula,

  $m=\frac{953-654}{68-45}$

So,

  $m=\frac{299}{23}$

On solving,

  $m=13$

Substituting the values in equation of line in slope point form,

  $y-953=13(x-68)$

To convert it into slope intercept form, Opening the brackets,

  $y-953=13x-884$

Shifting left-hand side values to right hand side,

  $y=13x-884+953$

On solving,

  $y=13x+69$

Hence, the equation of line is $y=13x+69$

Conclusion:

The equation of line is $y=13x+69$

b.

To determine

To evaluate slope and y-intercept

Answer to Problem 4.5STP

Slope is 13 and y-intercept is 69

Explanation of Solution

Given information:Serving 45 people the bill is $654

Serving 68 people the bill is $953

The equation of line is $y=13x+69$

Concept Used:equation of line is,

  $y=mx+c$

Calculation:

Comparing the given equation to the equation of line.

Slope is 13 and y-intercept is 69.

The slope represents the rate of change in y. Hence, in this case slope represents price of serving one person.

The y-intercept represents the initial value that is when the x is zero. Hence, in this case the y-intercept represents the basic charge the caterers take.

Conclusion:Slope is 13 and y-intercept is 69

c.

To determine

To calculate the number of people that can be served

Answer to Problem 4.5STP

79 people can be served in the budget of $1100

Explanation of Solution

Given information: Serving 45 people the bill is $654

Serving 68 people the bill is $953

The equation of line is $y=13x+69$

The budget is $1100

Concept Used: Solving the equation

Calculation:

Substituting the values in equation,

  $1100=13x+69$

Shifting right-hand side values to left hand side.

  $1100-69=13x$

So,

  $1031=13x$

On cross multiplying,

  $x=\frac{1031}{13}$

On solving

  $x=79.3$

Rounding off,

  $\approx 79$

Hence, 79 people can be served in the budget of $1100

Conclusion: 79 people can be served in the budget of $1100