# Equation

A commuter airline sells tickets for a flight at three rates: full fare, half far (for children), and early booking reduced fare (no further reduction for children). Fifty full fare, 12 half fare and 46 reduced fare tickets are sold for a total of $18,600. The reduced rate is $25 less than the half fare rate. Find the three rates.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

A commuter airline sells tickets for a flight at three rates: full fare, half far (for children), and early booking reduced fare (no further reduction for children). Fifty full fare, 12 half fare and 46 reduced fare tickets are sold for a total of $18,600. The reduced rate is $25 less than the half fare rate. Find the three rates.

Let the full fare be = x

Then the half fare would be x/2

Reduced fare is $ 25 less than the half fare rate

Therefore reduced fare = (x/2 -25)

Fifty full fare, 12 half fare and 46 reduced fare tickets are sold for a total of $18,600.

This means 50 * x + 12 * (x/2) + 46 * ( x/2-25) = 18600

( * indicates multiplication)

50 * x + 12 * (x/2) + 46 * ( x/2-25) = 18600

Simplifying

50 x + 6 x + 23 x - 1150 = 18600

or

79 x - 1150 = 18600

or

79 x = 18600+ 1150= 19750

0r x= 19750/79= 250

Thus x= full fare= 250

x/2= half fare= 250/2= 125

x/2-25= reduced fare= 125-25= 100

Answer: full fare= 250 , half fare= 125 , reduced fare= 100

check

50 full fare + 12 half fare + 46 reduced fare = 50 * 250 + 12 * 125 + 46 * 100 =

= 12500 + 1500 + 4600 = 18600

https://brainmass.com/math/algebra/equations-reduced-fare-tickets-22459