Answer to Question #176876 in Algebra for Mary Mao

Question

Two catering firms are competing for the catering contract for the school formal
dinner. Conya Cuisine has quoted a fixed charge of K450 plus K11 per head. Fred’s
Food has quoted a fixed charge of K300 plus K12.20 per head.
i) Identify the variables and denote them with a pro-numeral.
ii) Derive the equations involving the pro-numerals.
iii) Solve the equations. What practical information is given by your solution?
iv) If 250 students are attending the dinner, which company would be cheaper?
v) How many students need to attend for the catering costs to be equal

Answer 1

i) Let $x=$ the number of attenders, $y=$ the catering costs in kronos.

ii) Conya Cuisine has quoted a fixed charge of K450 plus K11 per head

$$y_C=450+11x$$

Fred’s Food has quoted a fixed charge of K300 plus K12.20 per head

$$y_F=300+12.20x$$

iii) If number of attenders is given, then we can determine the cost of dinners offered by Conya Cuisine $y_C$ and the cost of dinners offered by Fred’s Food 

$y_F.$

If the total the cost of dinners $y$ is given we can determine the possible number of attenders serviced by Conya Cuisine $x_C$ and the possible number of attenders serviced by Fred’s Food $x_F.$

$$x_C=\dfrac{y-450}{11}$$

$$x_F=\dfrac{y-300}{12.20}$$

iv) Given $x=250$

$$y_C=450+11(250)=3200$$

$$y_F=300+12.20(250)=3350$$

Since $y_C=3200<3350=y_F,$ then Conya Cuisine would be cheaper.

v) For the catering costs to be equal

$$y_c=y_F$$

$$450+11x=300+12.20x$$

$$12.20x-11x=450-300$$

$$1.20x=150$$

$$x=\dfrac{150}{1.20}$$

$$x=125$$

If 125 students are attending the dinner, the catering costs will be equal.

If we attend less than 125 students, then Fred’s Food would be cheaper.

If we attend more than 125 students, then Conya Cuisine would be cheaper.