Question: An Opera house collected $9,280 by selling tickets. The people sitting in the row A are charged $14 and the people sitting in row B are charged $12. The total number of tickets sold is 710. Find the number of people sitting in row A and row B.
A ) 380 in row A, 330 in row B B ) 379 in row A, 331 in row B C ) 331 in row A, 379 in row B D ) 330 in row A, 380 in row B
Steps to derive
1 Number of people in row A = x
2 Number of people in row B = y
3x + y = 710 --- (1) [Linear Equation for the people sitting in row A and row B.]
4 14x + 12y = 9280 --- (2) [Equation for the money collected by selling tickets.]
[Revised Equation 1.] 5y = 710 - x
[Replace y with 710 - x in Equation 1.] 6 14x + 12(710 - x) = 9280
[Combine like terms.] 7 2x + 8520 = 9280
[Subtract 8520 from both sides.] 8 2x = 760
[Divide each side by 2.] 9x = 380
[Substitute x = 380 in the revised Equation 1.] 10y = 710 - 380 = 330
11 The number of people sitting in row A are 380 and the number of people sitting in the row B are 330.
