Question

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Answer 1

`20*13=260` economy class seats
`20*5=100` business class seats

Explanation:

The ratio 13:5 describes the relationship between the economy and business class seats. First, add these numbers together to get `18`. Now, `360/18=20`, so we know there are 20 complete groups of seats. Therefore, each class of seats will be 20 times its respective number.
`20*13=260` economy class seats
`20*5=100` business class seats

`260+100=360` Check
`260/100=13/5` Check

Answer 2

There are 260 seats in economy class and 100 seats in business class.

Explanation:

Use two equations with two variables.

First, we know that the total number of seats on the plane is 360 seats.

Define variables:
`"Let " B " be the number of business class seats, and "`
`"let " E " be the number of economy class seats"`

`color(blue)(E+B=360)`

Our second equation is defined by rewording the second sentence of the problem. The problem basically states that the number of business class seats is `5/13` times the number of economy class seats. In equation form:

`color(blue)(B = 5/13 * E)`

Use substitution to solve for `B` and `E` - substitute the second equation into the first:

`E + (frac{5}{13}*E) = 360`

`(18/13)*E =360`

`E = 360 * 13/18`

`color(green)(E = 260" seats in economy class")`

More substitution:
`B = 5/13 * (260)`

`color(green)(B = 100" seats in business class")`