SOLUTION: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult plus a reservation charge that is the same on the child's ticket a

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Question 1208465: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult
plus a reservation charge that is the same on the child's ticket as on the adult's ticket.
One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult
and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
~~~~~~~~~~~~~~~~~~~ 

Let x be the basic fare for one way ticket for an adult (reservation is not included).

Then the basic fare for one way ticket for a child is x/2.


The reservation for an adult for this trip costs (216-x) dollars,
same as the reservation for a child.


Now the equation for the cost of the reserved ticket for an adult and the reserved ticket for a child is

    216 + x%2F2%29 + (216-x) = 327  dollars.


This equation is your setup. As soon as you got it and as soon as 
you do understand it, half of the problem is just solved.


To solve it to the end, simplify this equation and find x

    x%2F2 + (216-x) = 327 - 216

    x%2F2 + 216 - x =    111

    -x%2F2 = 111 - 216

    -x%2F2 =   -105

        x      =    2*105 = 210.


ANSWER.  The basic fare for the journey for an adult is $210.

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The cost of the air fare for a child is half the cost for an adult. So

let x = air fare for a child
then 2x = air fare for an adult

let y = reservation charge for either an adult or a child

Then...

One air fare for an adult with the reservation charge is $216:
2x%2By=216 [1]

The air fare for an adult and a child, with the reservation charges for both, is $327:
2x%2Bx%2By%2By=327
3x%2B2y=327 [2]

Equations [1] and [2] give you a system of two equations that is easily solved by standard algebraic methods.

However, this particular system of equation is easily solved by non-standard methods.

Comparing the two equations (i.e., finding the difference between [1] and [2]), we find

x%2By=111 [3]

Then, comparing equations [1] and [3], we find

x=105 [4]

ANSWER: the basic air fare for an adult is 2x = $210.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?

Let regular basic fare for an adult be A
Then regular basic fare for a child  = A%2F2 <=== The basic one-way air fare for a child aged between 3 and 10 years
                                               costs half the regular basic fare for an adult. 
Let reservation charge be R
Then cost of one reserved ticket for an adult = A + R = 216 ----- eq (i)
Since the cost of a reserved ticket for an adult and a child is $327, then cost of a reserved ticket for a child is
$327 - $216 = $111, and the cost EQUATION for a child's reserved ticket is: matrix%281%2C3%2C+A%2F2+%2B+R%2C+%22=%22%2C+111%29 ----- eq (ii)

                                     
                                       matrix%282%2C3%2C+A+-+A%2F2%2C+%22=%22%2C+105%2C+A%2F2%2C+%22=%22%2C+105%29 ----- Subtracting eq (ii) from eq (i)
Regular basic fare for an adult, or A = $210 ----- Cross-multiplying