Tickets to a basketball game cost $3 for students and $5 for non-students. The booster club reports they admitted 259 fans into the game and collected $831 by the end of the night. Determine how many student and adult fans bought tickets. Which 2 equations represent the system of equations for this scenario?
Let x = students and y = nonstudents. The total number of admitted fans = x + y = 259. The total in money spent would therefore be 3x + 5y = 831.
Your equations:
x + y = 259
3x + 5y = 831
Solve for y by multiplying the 1st equation by 3 and subtracting:
3x + 5y = 831
- (3x + 3y = 777)
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0x + 2y = 54 => y = 27
Since x + y = 259 and y = 27, x = 259 - 27 = 232.
232 students and 27 nonstudents bought tickets.
