Question: An Opera house collected $10,340 by selling the tickets. The people sitting in the row A are charged $16 and the people sitting in row B are charged $13. The total number of tickets sold is 710. Find the number of people sitting in row A and row B.
A ) 370 in row A, 340 in row B B ) 369 in row A, 341 in row B C ) 341 in row A, 369 in row B D ) 340 in row A, 370 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 16x + 13y = 10340 --- (2) [Equation for the money collected by selling tickets.]
[Revise Equation 1.] 5y = 710 - x
[Replace y with 710 - x in Equation 1.] 6 16x + 13(710 - x) = 10340
[Combine like terms.] 7 3x + 9230 = 10340
[Subtract 9230 from both sides.] 8 3x = 1110
[Divide each side by 3.] 9x = 370
[Substitute x = 370 in the revised Equation 1.] 10y = 710 - 370 = 340
11 The number of people sitting in row A are 370 and the number of people sitting in the row B are 340.
