Answer
Housing: $6133$,
Vehicles: $2269$
Health care: $5438$
Work Step by Step
First let's arrange the equation,
let $x$ denotes spending on housing, $y$ denote spending on vehicles/gas, $z$ denotes spending on health care.
Therefore, $x+y+z=13840$,
$x-y=3864$,
$x-z=695$,
Adding $x-y=3864$ and $x-z=695$ will result in $2x-y-z=4559$.
Arranging the equation again,
{$x+y+z=13840$
{$2x-y-z=4559$
adding the equation,
$3x=18399$,
$x=6133$,
substituting back in,
$6133-y=3864$,
$y=2269$,
substituting back in,
$6133-z=695$,
$z=5438$,
Therefore, the average per person spending on housing is $6133$, spending on vehicles is $2269$ and spending on health care is $5438$
