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One evening 1500 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28500. How many of each type of ticket were sold? Use substitution or elimination.

Answer :

Answer:

Tickets of lawn seat sold = 900

Tickets of pavilion seat sold = 600

Explanation:

Let [tex]x[/tex] be the no. of lawn seats and [tex]y[/tex] be the no. of pavilion seats.

According to the given question,

[tex]x + y = 1500[/tex]            ----eq 1  and

[tex]15x + 25y = 28500[/tex]  ---- eq 2

After obtaining the two equations we can solve this by either substitution or elimination.

By substitution, put

[tex]x = 1500 - y[/tex]   from eq 1 to eq 2, and solve for y, which gives

[tex]y = 600[/tex] and then substitute this value in eq 1 to get

[tex]x = 900[/tex]

By elimination, make the coefficient of one variable say x equal in both equations, for this multiply eq 1 with 15

now eq 1 becomes

[tex]15x + 15y = 22500[/tex] subtract this equation from eq 2 to get

[tex]y = 600[/tex] and substitute this value in eq 1 to get

[tex]x = 900[/tex]

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