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Chapter 4: Q. 343 (page 522)

Margie is planning a dinner banquet. The equation C=750+42gmodels the relation between the cost in dollars, C of the banquet and the number of guests, g.

(a) Find the cost if the number of guests is 50 .

(b) Find the cost if the number of guests is 100 .

(c) Interpret the slope and C-intercept of the equation.

(d) Graph the equation.

Short Answer

Expert verified
  1. The cost $2850if the number of guests is50.
  2. The cost $4950if the number of guests is 100.
  3. The slope mis 42, which means C will increase by 42 dollars when the number of gthat is guest increases by 1 . The C-intercept is 750 it means, when the guest gis 0 the cost Cwill be 750 .
  4. The graph is shown below:

Step by step solution

01

Given information

The given equation is C=750+42g.

02

Determine the value C when g=50 and g=100.

Substitute 50for gin the given equation.

C=750+42(50)=2850

Substitute 100for gin the given equation.

C=750+42(100)=4950

03

Determine the slope and intercept and then graph the equation.

Compare C=750+42gwith y=mx+bwhere mbe the slope and y-intercept.

m=42and b=750

The graph is shown below:

04

Write the conclusion

  1. The value of Cwhen g=50is 2850.
  2. The value of Cwhen g=100is 4950.
  3. The slope is 42and the C-intercept is 750.
  4. The graph is shown below:

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