3.2 The Student Representative Council (SRC) is organising a concert. They need
to generate exactly R6000 in revenue from ticket sales to cover the sound
equipment costs.
Let 𝑥𝑥 be the price of one ticket. Let 𝑦𝑦 be the number of people attending. The
current situation is represented by the equation 𝑥𝑥𝑥𝑥 = 6000.
The SRC realises that if they lower the ticket price by R10, they will attract 20
more people to the concert. The total revenue would remain exactly R6000.
3.2.1 Set up a system of two equations to represent this situation. (4)
3.2.2 Substitute one variable into the other to show that this situation results in
the quadratic equation: 𝑥𝑥2 − 10𝑥𝑥 − 3000 = 0 (or a variation depending on
your substitution). (5)
3.2.3 Solve for the original price of the ticket (𝑥𝑥). Explain why the negative
solution is mathematically valid for the equation but not valid in the
context. (6)
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