Answer to Question #176999 in Linear Algebra for Anzena

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

Solution.

i)$x=$ the number of attenders, $y=$ the catering costs, K.

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 $y_F.$

$$x_C=\dfrac{y-450}{11}$$ $$x_F=\dfrac{y-300}{12.20}$$

iv) If $x=250$

$$y_C=450+11(250)=3200 K$$ $$y_F=300+12.20(250)=3350 K$$

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

v)

$$y_c=y_F$$ $$450+11x=300+12.20x$$ $$12.20x-11x=450-300$$ $$1.20x=150$$ $$x=\dfrac{150}{1.20}$$ $$x=125$$

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