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Two baseball teams have a game Monday night. Within the first minute, they sell 7 adult tickets and 13 student tickets for a total of $146. The next minute they sell $276 worth of tickets by selling 14 adult tickets and 24 student tickets. Create a system of equations to model the scenario. Determine the cost of one adult ticket and one student ticket. Use mathematics to justify your answer.

Two Baseball Teams Have A Game Monday Night Within The First Minute They Sell 7 Adult Tickets And 13 Student Tickets For A Total Of 146 The Next Minute They Sel class=

Sagot :

Answer:

The cost of one adult ticket is $6 and the cost of one student ticket is $8.

Explanation:

Let the cost of one adult ticket=a

Let the cost of one student ticket=s

They sell 7 adult tickets and 13 student tickets for a total of $146.

[tex]7a+13s=146[/tex]

They sell $276 worth of tickets by selling 14 adult tickets and 24 student tickets.

[tex]\implies14a+24s=276[/tex]

Thus, the system of equations to model the scenario is:

[tex]\begin{gathered} 7a+13s=146 \\ 14a+24s=276 \end{gathered}[/tex]

Multiply the first equation by 2 and the second by 1.

[tex]\begin{gathered} 14a+26s=292 \\ 14a+24s=276 \end{gathered}[/tex]

Subtract:

[tex]\begin{gathered} 2s=16 \\ s=\frac{16}{2} \\ s=8 \end{gathered}[/tex]

Next, we solve for 'a' using any of the equations.

[tex]\begin{gathered} 7a+13s=146 \\ 7a+13(8)=146 \\ 7a+104=146 \\ 7a=146-104 \\ 7a=42 \\ a=\frac{42}{7} \\ a=6 \end{gathered}[/tex]

Therefore, the cost of one adult ticket is $6 and the cost of one student ticket is $8.

Check

[tex]\begin{gathered} 7a+13s=146 \\ 7(6)+13(8)=146 \\ 42+104=146 \\ 146=146 \end{gathered}[/tex]

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