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Question 250074: You are selling tickets for a high school basketball game. Student
tickets cost $3 and general admission tickets cost $5. You sell 350
tickets and collect $1,450. How many student tickets did you sell?
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! You are selling tickets for a high school basketball game. Student
tickets cost $3 and general admission tickets cost $5. You sell 350
tickets and collect $1,450. How many student tickets did you sell?
This can be solved as a system of two equations:
Student tickets cost $3 and general admission tickets cost $5. You sell 350
tickets. Therefore, the first equation is:
Student Tickets (S) + Genr'l Admission Tickets (G) = 350
S + G = 350
The second equation is: S(3.00) + G(5.0) = 1,450
The two equations are:
S + G = 350 ------> this is also the same as: S = 350 - G (Substitute this info into the 2nd equation).
S(3.00) + G(5.0) = 1,450
S(3.00) + G(5.0) = 1,450 (original 2nd equation)
3.00(350 - G) + G(5.0) = 1,450 (Plugged S = 350 - G into the equation)
1,050 - 3.0G + G(5) = 1,450 (distributed the 3.0 to the 350 and to the G)
1,050 + 2.0G = 1,450 (combined -3.0G + G5 to get 2.0G)
2.0G = 1,450 - 1,050 (subtracted 1,050 from both sides to isolate G)
2.0G = 400
G = 200 (divided both sides by 2.0 to isolate the G)
Now we know there were 200 general admission tickets. Let's go back to the 1st equation:
S + G = 350
S + 200 = 350 (substituted in the 200 for the G variable)
S = 350 - 200 (subtracted 200 from both sides of the equation to isolate the S)
S = 150
Does this work out? Let's check..........
You are selling tickets for a high school basketball game. Student
tickets cost $3 and general admission tickets cost $5. You sell 350
tickets and collect $1,450.
150 Student tickets + 200 Gen Admission tickets = 350 so that checks.
200(5) + 150(3) =
1000 + 450 = 1,450 This checks, too.
Hope this helps. :-)
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