Answer to Question #116987 in Linear Algebra for Me

Question

Western Air sold twenty-seven airline tickets to Cape Town on a certain day. Each Economy class ticket (E) was sold at N$3200 and the First-class tickets (F) were sold at N$4100 each. The total amount received for the twenty-seven tickets was N$92700.
4.5.1 Formulate the above information into two linear equations [2]
4.5.2 Solve these equations simultaneously using the substitution method and calculate the number of first-class tickets sold. [6]

Answer 1

4.5.1 Let $x$ be the number of Economy class tickets and $y$ be the number of the First-class tickets. The total number will be

$x+y=27$ .

The total amount of money will be

$3200\cdot x + 4100\cdot y = 92700.$

Therefore, the linear system is

$\begin{cases} x+y=27 \\ 3200\cdot x + 4100\cdot y = 92700. \end{cases}$

4.5.2 Let us divide the second equation by 100, for convenience, so we get

$\begin{cases} x+y=27 \\ 32\cdot x + 41\cdot y = 927. \end{cases}$

Next, we express $x$ from the first equation and substitute it into the second:

$\begin{cases} x=27-y \\ 32\cdot(27-y) + 41\cdot y = 927. \end{cases}$

We should solve the second equation

$\begin{cases} x=27-y \\ 32\cdot27 + 9\cdot y = 927. \end{cases}$

$\begin{cases} x = 27-y,\\ y=7. \end{cases}$

$\begin{cases} x = 20,\\ y=7. \end{cases}$

Therefore, the number of First-class tickets is 7.