Question

1. In 2003, gross sales at McDonald’s and Burger King totaled $60.9 billion. McDonald’s sales exceeded Burger King’s sales by $22.1 billion.

(a) Write a system of equations whose solution gives the individual sales of each company in billions of dollars.

(b) Solve the system of equations. (c) Is your system consistent or inconsistent? If it is consistent, state whether the equations are dependent or independent.

2. Solve the system symbolically 3x-2y=5 x+5y=13

3. Answer the following questions

a. What is a matrix?

b. What is a matrix Dimension

c. What is a matrix element?

Answer 1

1. (a). Let the gross sales at McDonald’s and Burger King, in 2003, be $ x billion and $ y billion respectively. Then, x+y = 60.9…(1) and x = y+22.1…(2)

(b).On substituting x = y+22.1 in the 1^st equation, we get y+22.1 +y = 60.9 or, 2y = 60.9-22.1 = 38.8 so that y = 38.8/2 = 19.4. Then x = 19.4+22.1 = 41.5. Thus, in 2003, the gross sales at McDonald’s and Burger King were $ 41.5 billion and $ 19.4 billion respectively.

2.   The two given equations are consistent and the solution is = 3, and y = 2. From the 2^nd equation, we have x = 13-5y so that symbolically, a solution is (x,y) = (13-5a,a). If we start with the 1^st equation, then   we have 3x= 2y+5 or, x = (2y+5)/3 so that (x,y) = ( (2a+5)/3,a ) is symbolically a solution.

3. (a). A matrix is a rectangular/square array of numbers.

(b). The dimension of a matrix is defined by its number of rows and columns. A matrix with m rows and n columns is called a m × n matrix and m and n are called its dimensions.

( c). The numbers/expressions/symbols in a matrix are called its elements.