SOLUTION: There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought

Question 57328: There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?
Let a = the number of adult tickets purchased.
Let s = the number of student tickets purchased. Write a system of equations that can be used to determine the number of adult and student tickets purchased.
Determine the number of adults tickets sold and the number of student tickets sold.

Found 3 solutions by CrazyMan Jr., funmath, stanbon:
Answer by CrazyMan Jr.(21)   (Show Source): You can put this solution on YOUR website!
2s+3.5a = 3825
s+a = 1500
2s+3.5a = 3825 1.5a = 825
2s+2a = 3000 1.5a/1.5 = 825/1.5 a = 550
Sub In
2s+3.5(550) = 3825
2s+1925 = 3825
2s = 1900
s = 950
Sub In Again
950+550 = 1500
1500 = 1500
Therefore, 550 adult tickets & 950 student tickets were purchased.
J-Man

Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
If you are the same person I answered earlier, you wanted a system of two equations and two unknowns. If you aren't and you only want one equation and one unknow, let me know.
There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?
Let a = the number of adult tickets purchased.
Let s = the number of student tickets purchased. Write a system of equations that can be used to determine the number of adult and student tickets purchased.
Determine the number of adults tickets sold and the number of student tickets sold.
:
The total number of adults, a, and students, s, is 1500.
a+s=1500
The total amount of money taken in per adult is $3.50*a, the amount of money taken in per student is $2.00s, which totals $3825.
3.50a+2.00s=3825
The system of equations is:
a+s=1500
3.50a+2.00s=3825
:
Solve the first equation for a and substitute that into the second equation and solve that equation for s:
a+s=1500
a=1500-s

5250-3.50s+2.00s=3825
5250-1.50s=3825
-1.50s=3825-5250
-1.50s=-1425
-1.50s/-1.50=-1425/-1.50
s=950
Substitute s=950 into the first equation and solve for a.

a=1500-950
a=550
Theref were 550 adults and 950 students.
Happy Calculating!!!
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?
Let a = the number of adult tickets purchased.
Let s = the number of student tickets purchased. Write a system of equations that can be used to determine the number of adult and student tickets purchased.
Determine the number of adults tickets sold and the number of student tickets sold.
1st: a+s=1500
2nd: 3.5a+2s=3825
Solve 1st for a and substitute in 2nd to get:
3rd: 3.5(1500-s)+2s=3825
5250-3.5s+2s=3825
-1.5s=-1425
s=950 (number of students tickets sold)
Substitute into 1st to solve for "a":
a+950 = 1500
a=550 (number of adult tickets sold)
Cheers,
Stan H.

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