Question 1208465
<br>
The cost of the air fare for a child is half the cost for an adult. So<br>
let x = air fare for a child
then 2x = air fare for an adult<br>
let y = reservation charge for either an adult or a child<br>
Then...<br>
One air fare for an adult with the reservation charge is $216:
{{{2x+y=216}}} [1]<br>
The air fare for an adult and a child, with the reservation charges for both, is $327:
{{{2x+x+y+y=327}}}
{{{3x+2y=327}}} [2]<br>
Equations [1] and [2] give you a system of two equations that is easily solved by standard algebraic methods.<br>
However, this particular system of equation is easily solved by non-standard methods.<br>
Comparing the two equations (i.e., finding the difference between [1] and [2]), we find<br>
{{{x+y=111}}} [3]<br>
Then, comparing equations [1] and [3], we find<br>
{{{x=105}}} [4]<br>
ANSWER: the basic air fare for an adult is 2x = $210.<br>