Make an equation system based on the problem
An equation for "A plane has 360 total seats, which are divided into economy class and business class" is
∴ e + b = 360 (first equation)
"For every 13 seats in economy class, there are 5seats in business class" that means in 1b there is (5/13) e
∴ [tex]b= \frac{5}{13} e[/tex] (second equation)
Solve the equation, find the value of e
Subtitute b with (5e)/13 in the first equation
e + b = 360
[tex] e + \frac{5e}{13} = 360[/tex]
Equalize the denominators
[tex] \frac{13e}{13} + \frac{5e}{13} =360[/tex]
[tex] \frac{18e}{13}=360[/tex]
move 13 to the right side, and solve for e
[tex] \frac{18e}{13}=360[/tex]
18e = 360 × 13
18e = 4,680
e = 4,680/18
e = 260
Find the value of b
e + b = 360
260 + b = 360
b = 360 - 260
b = 100
There are 260 seats in economy class and 100 seats in business class
