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A concert venue sold 8000 tickets for a total revenue of 250,000. VIP tickets cost 50 and popular stand tickets cost $30. How many of each type of ticket were sold?

Mathematics

ScanSolve AI Answer

Step-by-step solution

5 steps
  1. Define variables and set up equations based on the given information.

    Let VV be the number of VIP tickets sold and PP be the number of popular stand tickets sold.
    We are given:

    • Total number of people: 8000
    • Price of VIP ticket: \50$
    • Price of popular stand ticket: \30$
    • Total revenue: \250,000$

    From this, we can form two equations:

    V+P=8000(Equation 1)V + P = 8000 \quad \text{(Equation 1)} 50V+30P=250000(Equation 2)50V + 30P = 250000 \quad \text{(Equation 2)}
  2. Solve Equation 1 for PP in terms of VV.

    P=8000−VP = 8000 - V
  3. Substitute the expression for PP into Equation 2.

    50V+30(8000−V)=25000050V + 30(8000 - V) = 250000 50V+240000−30V=25000050V + 240000 - 30V = 250000
  4. Simplify and solve for VV.

    20V+240000=25000020V + 240000 = 250000 20V=250000−24000020V = 250000 - 240000 20V=1000020V = 10000 V=1000020V = \frac{10000}{20} V=500V = 500
  5. Substitute the value of VV back into the expression for PP.

    P=8000−VP = 8000 - V P=8000−500P = 8000 - 500 P=7500P = 7500

    The number of VIP tickets sold is 500 and the number of popular stand tickets sold is 7500.

    VIP tickets: 500, Popular stand tickets: 7500\boxed{\text{VIP tickets: } 500, \text{ Popular stand tickets: } 7500}
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