# In the following case let x = number of student tickets and y=number of regular tickets. Write a system of 4 inequalites modeling their possible ticket purchases. Nathan and his friends want to go...

In the following case let x = number of student tickets and y=number of regular tickets. Write a system of 4 inequalites modeling their possible ticket purchases.

Nathan and his friends want to go to a hockey game. Tickets are $18 each, but students can get discounted tickets at $12. They want to spend no more than $80, including $8 for parking. The car they will take can only hold 7 people.

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### 1 Answer

Nathan and his friends go to a hockey game. The total number of people going to the game is x + y where x is the number of students and y is the number of people that are not students.

As the car can only hold 7 people, the first inequality we have is `x+y <= 7`

The maximum amount that Nathan and his friends want to spend is $80. This includes $8 for parking. The cost of regular tickets is $18 and students can buy tickets for $12. The total amount spent on buying tickets is 18*x + 12*y. This cannot exceed $72, the next inequality is `12*x + 18*y <= 72`

=> `2x + 3y <= 12`

If all those that go are students the cost of the tickets is 12*x. This gives `12*x <= 72`

=> `x <= 6`

Similarly, if all those that go have to buy regular tickets `18*y < 72`

=> `y<= 4`

**The four inequalities that apply with the information provided are `x + y <= 7` , `2x + 3y <= 12` , `x <= 6` and `y <= 4` **

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Very hepful Thanks! :)