a)
The linear equation in standard form is expressed as
Ax + By = C
where
A, B and C are constants
x and y are variables. In the given scenario, Let x represent the cost of each CD and y represent the cost of each book. Each CD costs $8 and each book costs $6. You have $96 to spend. This means that the total cost of the CDs and books would be 96. By comparing with the standard equation,
A = 8
B = 6
C = 96
The equation modelling this situation is
8x + 6y = 96
b)If you purchase 4 books, we woud find the number of CDs you can purchase by substituting y = 4 into the equation. We have
8x + 6 * 4 = 96
8x + 24 = 96
Subtracting 24 from both sides of the equation, wehave
8x + 24 - 24 = 96 - 24
8x = 72
dividing both sides of the equation by 8, we have
8x/8 = 72/8
x = 9
You can purchase 9 CDs
