Question

19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?​

Answer 1

a. To write a linear system that represents this situation, we can use the information given in the problem to create two equations. Let x represent the cost of one adult ticket and y represent the cost of one youth ticket. Then:

- For the first family: 2x + 4y = 28
- For the second family: 4x + 5y = 45.50

b. To solve this linear system, we can use the elimination method. We can multiply the first equation by -2 and add it to the second equation to eliminate the term for 4x:

-2(2x + 4y = 28) -> -4x - 8y = -56
4x + 5y = 45.50
_____________
-3y = -10.50
y = 3.50

Now, we can substitute this value of y into either equation to solve for x. Let's use the first equation:

2x + 4(3.50) = 28
2x + 14 = 28
2x = 14
x = 7

Therefore, the cost of one adult ticket is $7 and the cost of one youth ticket is $3.50.

c. To find out how much it would cost two adults and five youths to attend the game, we can simply multiply the cost of each ticket by the number of tickets:

2 adults * $7/adult ticket = $14
5 youths * $3.50/youth ticket = $17.50

Therefore, it would cost two adults and five youths a total of $31.50 to attend the game.