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There are two types of tickets sold at the Canadian Formula One Grand Prix race. The price of 5 grandstand tickets and 3 general admission tickets is 2490. The price of 6 grandstand tickets and 6 general admission tickets is 3540 . What is the price of each type of ticket?

User Allison Lock
by
2.9k points

2 Answers

17 votes
17 votes

Answer: Grandstand: 360, General Admission: 230

Explanation:

Use any variable you like but:

  • Let g represent grandstand tickets
  • Let a represent general admission tickets

You know:

5 Grandstand tickets and 3 general admission tickets is 2490:

  • 5g + 3a = 2490

The price of 6 grandstand (g) tickets and 6 general admission tickets (a) is 3540

  • 6g + 6a = 3540

You want to find out: What is the price of each ticket. To do this either use substitution or elimination.

I will demonstrate elimination:

To do elimination, you want to cancel out one variable. This means you want to multiply each side of the equation by a number. I see 3a and 6a. This means multiply by -2. Again, you want to eliminate the variable.

  • 5g +3a = 2490 → -10g - 6a = -4980

Now, add the two equations together: Notice how you can line them up vertically to see how they can add together.

  • -10g - 6a = -4980
  • +6g + 6a = 3540
  • After that step you get: -4g = -1440

Now you can solve for the g (grandstand tickets):

  • -4g = -1440
  • g = 360

You now know grand stand tickets cost 360. Take one of your original equations and solve for a (general admission tickets). To double check your work, they should satisfy both equations.

  • 5g + 3a = 2490
  • 5(360) + 3a = 2490
  • 3a = 690
  • a = 230
  • 6g +6a = 3540
  • 6(360) +6a = 3540
  • 6a = 1380
  • a = 230

Therefore general admission tickets cost 230, and grandstand tickets cost 360!

User Planet X
by
2.2k points
22 votes
22 votes
General admission tickets are $287.50 each and grandstand tickets are $311.25 each
User Fayakon
by
3.0k points
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