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Three types of tickets for a football game are​ available: sidelines,​ goal-view, and​ upper-deck. The sidelines tickets cost ​$25 more than the​ goal-view tickets and ​$50 more than the upper deck tickets. The​ goal-view tickets cost ​$13 less than twice the cost of the​ upper-deck tickets. Determine the price of each type of ticket.

Respuesta :

MrRoyal

Answer:

Upper deck = $38

Goal View = $63

Sidelines = $88

Step-by-step explanation:

Represent

- Sidelines with S

- Goal-view with G

- Upper-deck with U

We have that:

[tex]S = 25 + G[/tex]

[tex]S = 50 + U[/tex]

[tex]G = 2U - 13[/tex]

Required

Solve for S, G and U

Substitute 25 + G for S in the second equation

[tex]25 + G = 50 + U[/tex]

Make G the subject

[tex]G = 50 -25+ U[/tex]

[tex]G = 25+ U[/tex]

Substitute 25 + U for G in the third equation

[tex]25 + U = 2U - 13[/tex]

Collect Like Terms

[tex]U - 2U = -13 - 25[/tex]

[tex]-U = -38[/tex]

[tex]U = 38[/tex]

Substitute 38 for U in [tex]G = 25+ U[/tex]

[tex]G = 25 + 38[/tex]

[tex]G =63[/tex]

Substitute 63 for G in [tex]S = 25 + G[/tex]

[tex]S = 25 + 63[/tex]

[tex]S = 88[/tex]

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