SOLUTION: There are 1500 sold tickets to an event. 25 dollars for covered seats and 15 dollars for uncovered seats. The total cost of all sold tickets is 28,500. How many covered and uncover

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Question 326897: There are 1500 sold tickets to an event. 25 dollars for covered seats and 15 dollars for uncovered seats. The total cost of all sold tickets is 28,500. How many covered and uncovered seats were purchased.
Found 2 solutions by Fombitz, jessica43:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let C be covered seats, U uncovered seats.
1.C%2BU=1500
.
.
25C%2B15U=28500
2.5C%2B3U=5700
Multiply eq.1 by -3 and add to eq. 2 to eliminate U.
-3C-3U%2B5C%2B3U=-4500%2B5700
2C=1200
highlight%28C=600%29
Then from above,
600%2BU=1500
highlight%28U=900%29

Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you are going to write two equations using what you know.
First, you know that the total number of tickets sold is 1500:
C + U = 1500 (where C = number of tickets for covered seats, U = number of tickets for uncovered seats)
This can be rewritten as C = 1500 - U
Second, you know that a covered seat ticket is $25 and an uncovered seat ticket is $15 and the total cost of the tickets is $28,500:
25(C) + 15(U) = 28500
Now plug in the rewritten first equation into the second equation and solve for U:
25(C) + 15(U) = 28500
25(1500 - U) + 15(U) = 28500
37500 - 25(U) + 15(U) = 28500
37500 - 10(U) = 28500
-10(U) = -9000
U = 900
So 900 tickets for uncovered seats were sold.
Now plug this into the first equation to find C:
C + U = 1500
C + 900 = 1500
C = 600
So 600 tickets for covered seats were sold.