Question

A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5seats in business class.
How many seats are there in each class?

Answer 1

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
∴ $b= \frac{5}{13} e$    (second equation)

Solve the equation, find the value of e
Subtitute b with (5e)/13 in the first equation
e + b = 360
$e + \frac{5e}{13} = 360$
Equalize the denominators
$\frac{13e}{13} + \frac{5e}{13} =360$
$\frac{18e}{13}=360$

move 13 to the right side, and solve for e
$\frac{18e}{13}=360$
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