Question 1208465
<pre>
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/2}}} <=== 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(1,3, A/2 + R, "=", 111)}}} ----- eq (ii)

                                     {{{system(matrix(1,6, A + R, "=", 216, "-----", eq, "(i)"),
matrix(1,6, A/2 + R, "=", 111, "-----", eq, "(ii)")))}}}
                                       {{{matrix(2,3, A - A/2, "=", 105, A/2, "=", 105)}}} ----- Subtracting eq (ii) from eq (i)
<font color = red><font size = 4><b>Regular basic fare for an adult</font></font></b>, or A = <font color = red><font size = 4><b>$210</font></font></b> ----- Cross-multiplying</pre>