Question

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?

Answer 1

General admission tickets are $287.50 each and grandstand tickets are $311.25 each

Answer 2

Answer: Grandstand: 360, General Admission: 230

Step-by-step 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!