Question

Two basketball teams have a game Friday night. Within the first minute, they sell 8 adult tickets and 12 student tickets for a total of $124. The next minute they sell $243 worth of tickets by selling 16 adult tickets and 23 student tickets. Create a system of equations to model the scenario. Determine the cost of a student ticket and an adult ticket. Use mathematics to justify your answer.

Answer 1

The cost of a student ticket and an adult ticket are $5 and $8 respectively.

We can solve the question above using simultaneous equation.

Let :

x = price of adult tickets

y = price of children tickets

If 8 adult tickets and 12 student tickets are sold for a total of $124, the first equation would be

8x + 12y = $124

If 16 adult tickets and 23 student tickets are sold for a total of $243, the second equation would be

16x +23y = $243

Then, the two equations are

8x + 12y = 124

16x +23y = 243

To solve, multiply equation 1 by 2 . This gives equation 3

16x + 24y = 248

Now substract equation 3 from 2.

This gives y = 5

To find y, substitute 5 with y in equation 1

8 x + 12(5) = 124

8x + 60 = 124

Collect like terms

8x = 124 - 60

8x = 64

Divide both sides by 8

x = 8

Hence, the price adult ticket is $8 while the price of children ticket is $5.

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