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:
<u>5 Grandstand tickets and 3 general admission tickets is 2490: </u>
The price of 6 grandstand (g) tickets and 6 general admission tickets (a) is 3540
<u>You want to find out</u>: What is the price of each ticket. To do this either use substitution or elimination.
<u>I will demonstrate elimination: </u>
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):
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!
