SOLUTION: An airplane was traveling with 480 passengers. When it arrived at the first airport, some passengers got off and 30 people got on an airplane. At the next airport, half the passeng

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: An airplane was traveling with 480 passengers. When it arrived at the first airport, some passengers got off and 30 people got on an airplane. At the next airport, half the passeng      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 958146: An airplane was traveling with 480 passengers. When it arrived at the first airport, some passengers got off and 30 people got on an airplane. At the next airport, half the passengers got off the plane and 70 people got on an airplane. There were now 220 passengers on an airplane.
a)Write the equation from the statement.
b)Find the number of passengers who came out off an airplane at the first airport.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
start with 480.

at the first airport, x got off and 30 got on.

the plane is left with 510 - x passengers.

at the next airport, half the passengers got off and 70 got on.

the plane is left with (510 - x) - (510 - x) / 2 + 70.

simplify by removing the parentheses to get that the plane is left with 510 - x - 255 + x/2 + 70 passengers.

simplify further by combining the constants to get that the plane is left with 325 - x + x/2 passengers.

simplify further by combining the variables to get that the plane is left with 325 - x/2 passengers.

you are told that the plane is left with 220 passengers.

this means that 325 - x/2 = 220

subtract 325 from both sides of this equation to get -x/2 = -105.

multiply both sides of this equation by -2 to get x = 210.

that's your solution.

210 passengers got off the plan at the first airport.

confirm your solution is correct.

start with 480 and add 30 and subtract 210 to get 300 passengers still on the plane when the plane leaves the first airport.

subtract half of 300 and add 70 to get 150 + 70 = 220 passengers still on the plane when the plane leaves the second airport.

solution is confirmed as correct.

solution is that 210 passengers got off the plane at the first airport.