# An airline flies from manila to davao with a stopover in cebu. it charges a fare of 1,800 pesos manila to cebu and a fare of 3,500 pesosfrom manila to davao. in one flight a total of 180 passengers boarded the plane in manila and the collected fare totalled 494,000 pesos. how many passengers got off the plane in cebu? â€‹

Step-by-step explanation:

Passengers:

To Cebu: x

To Davao: y

Total passengers: 180

Equation (1):

x + y = 180

y = 180 - x Â (passengers to Davao in terms of x)

Total fare:

Manila to Cebu: 1,800x

Manila to Davao: 3,500y

Total passenger fare for both destinations: Â 494,000

Equation (2):

1,800x + 3,500y = 494,000

Substitute 180-x to y in Equation (2):

1,800x + 3,500y = 494,000

1,800x + 3,500(180-x) = 494,000

Find the number of passengers to Cebu, x:

1,800x -3,500x + 630,000 = 494,000

-1700x = 494,000 - 630,000

-1700x/-1,700 = -136,000/-1700

x = 80 passengers to CebuNumber of passengers to Davao, y:

y = 180-x

y = 180 - 80

y = 100 passengers to DavaoTotal passenger fare for each destination:

Manila to Cebu:

1,800x = 1,800(80) = 144,000 pesos

Manila to Davao:

3,500y = 3,500(100) = 350,000 pesos

Check:

Total passengers:

80 + 100 = 180

180 = 180 Â (True)

Total fare:

144,000 + 350,000 = 494,000

494,000 = 494,000 (True)

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