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Question 828935: The attendance at a rock concert was 6700 people. The tickets for the concer cost $40 for floor seats and $25 for all other seats. The total income of ticket sales was $185,500. write a linear system that models this situation. Solve the system using Cramer's rule, using the substitution method, and using the elimination method. Compare the methods, and explain which one you perfer in this situation. I did the elimination and substitute methods, but I cannot figure out how to set up the Cramer part. Any help would be appreciated
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! x +y = 6700
40x +25y = 185500
we have a 2 by 2 matrix and single column solution vector
we calculate the determinant (D) of a two by two matrix according to this formula
| a b |
| c d |
D = ad - bc
for our linear system of equations, the matrix is
| 1 1 |
| 40 25 |
and D = (1*25) - (40*1) = -15
now we need to replace the x column with our column solution vector
| 6700 1 |
| 185500 25 |
Dx = (6700 * 25) - (185500 * 1) = -18000
now we need to replace the y column with our column solution vector
| 1 6700 |
| 40 185500 |
Dy = (1 * 185500) - (6700 * 40) = 185500 - 268000 = -82500
now x = Dx / D = -18000 / -15 = 1200
y = Dy / D = -82500 / -15 = 5500
we have 1200 tickets at $40 and 5500 at $25
check answer
1200 +5500 = 6700
6700 = 6700
also
(40*1200) + (25*5500) = 185500
48000 + 137500 = 185500
185500 = 185500
answer checks :-)
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