SOLUTION: An airline carries 180 passengers and 10 tonnes of freight and earns $75000 for its owners in fares and freight charges. On the return trip it carries 100 passengers and 20 tonnes
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Question 673180: An airline carries 180 passengers and 10 tonnes of freight and earns $75000 for its owners in fares and freight charges. On the return trip it carries 100 passengers and 20 tonnes of freight, earning $85000. What is the passenger fare per person and the freight charges per tonne.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
An airline carries 180 passengers and 10 tonnes of freight and earns $75000 for its owners in fares and freight charges. On the return trip it carries 100 passengers and 20 tonnes of freight, earning $85000. What is the passenger fare per person and the freight charges per tonne.
.
Let x = cost ($) per person
and y = cost ($) per ton
.
from:"180 passengers and 10 tonnes of freight and earns $75000"
180x + 10y = 75000
.
from:"100 passengers and 20 tonnes of freight, earning $85000"
100x + 20y = 85000
.
Our simultaneous equations:
180x + 10y = 75000
100x + 20y = 85000
.
multiply top equation by -2 and combine with second:
-360x - 20y = -150000
100x + 20y = 85000
------------------------
-260x = -65000
x = -65000/(-260)
x = $250 (passenger fare per person)
.
freight charges per tonne:
plug above into:
100x + 20y = 85000
100(250) + 20y = 85000
25000 + 20y = 85000
20y = 60000
y = $3000 (per tonne)
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