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2 Answers
May 16, 2018

#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

May 16, 2018

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")#