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 bough

Algebra ->  Matrices-and-determiminant -> 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 bough      Log On


   

Question 105146: 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?

Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
Lets call the number of student tickets x
and the number of adult tickets y
Now we are told that 1500 people attended the game. So...
x + y = 1500
Now we are also told that the total receipts for the game were $3825 and student tickets cost $2.00 and adult tickets cost $3.50. So...
2x + 3.5y = 3825
Ok so we have a system of equations:
x + y = 1500
AND
2x + 3.5y = 3825
We can solve for x and y by using the substitution method.
Start with the first equation and set it equal to x
x + y = 1500
x = 1500 - y
Now since we have shown that x is equal to 1500-y we can substitute 1500-y for x in the second equation
2x + 3.5y = 3825
2(1500-y) + 3.5y = 3825
3000 - 2y + 3.5y = 3825
3000 + 1.5y = 3825
1.5y = 825
y = 550
Answer: 550 Adults attended the game
Now use this value for y to solve for x
x + y = 1500
x + 550 = 1500
x = 950
Answer: 950 Students attended the game
Check answers in both equations
x + y = 1500
950 + 550 = 1500
1500 = 1500
------------
2x + 3.5y = 3825
2(950) + 3.5(550) = 3825
1900 + 1925 = 3825
3825 = 3825