Question

Passengers of flyaway airlines can purchase tickets for either business class or economy class. On one particular flight there were 154 passengers. Let x be the number of business class passengers and y be the number of economy class passengers on this flight.

Use the information above to write down an equation in x and y.

On this flight the cost of a ticket for each business class passenger was 320 euros and the cost of a ticket for each economy class passenger was 85 euros. The total amount that Flyaway Airlines received for these tickets was 14970 euros.

Use this information about the cost of the tickets to write down a second equation in x and y.

Find the value of x and the value of y.

The airlines finance officer write down the total amount received by the airline for these tickets as 14270 euros.

Find the percentage error.

Answer 1

x = 8

y = 146

Error = 4.86%

Explanation:

Number of business class passenger = x

and the economy class passenger = y

Total number of passengers = 154

x + y = 154 ------(1)

Cost of business class tickets and economy class tickets are €320 and €85 respectively.

Total amount received by airlines is €14970.

320x + 85y = 14970

64x + 17y = 2994 --------(2)

Multiply equation (1) by 17 and subtract from equation (2)

(64x + 17y) - (17x + 17y) = 2994 - 2618

47x = 376

x = 8

From equation (1),

8 + y = 154

y = 154 - 8

y = 146

Airline officer wrote down the amount received as €14270

Then difference from the actual amount received = 14970 - 14270

= €700

% Error =
`\frac{\text{Difference in amount}}{\text{Actual amount}}* 100`

=
`(700)/(14970)* 100`

= 4.676

≈ 4.68%

Therefore, x = 8 and y = 146

and % error = 4.68%