Please help me with this !

Question

An airplane has 173 seats. Seats on a flight to Albuquerque cost $675 in first class,

$590 in business class, and $480 in coach. The number of seats in coach is 9 more than 3 times

the total number of seats in first class and business class combined. If the airline takes in

$88,910 from a sold-out flight, how many seats does each section hold?

Answer 1

x = 1st class

y = business class

z = coach class

X+y+z = 173

z = 3(x+y)+9 = 3x+3y+9

675x + 590y + 480z = 88910

x + y + (3x+3y+9) = 173

675x + 590y + 480(3x+3y+9) = 88910

the first equation becomes:

4x + 4y = 164

x + y = 41 <--- first equation

the second equation becomes:

675x + 590y + 1440x + 1440y + 4320 = 88910

2115x + 2030y = 84590

substitution:

2115x + 2030 ( 41-x) = 84590

2115x + 83230 - 2030 x = 84590

85x = 1360

x = 16

which forces y = 25

which forces z = 132