Question 1030527
x, price for small dog
y, price for large dog


Putting attention on the second sentence:
half as much as the large dog if large dog were y-5...
Translates or transcribes as {{{something=(1/2)(y-5)}}}.


Small dog cost..., and that transcribed part:
{{{highlight_green(x=(1/2)(y-5))}}}.


The hard part is now taken out of the way, so deal with the first sentence.
{{{x+y=38}}}
and all you need to do is make the substitution for x, the expression described for the cost of the small dog in terms of the large dog price.


{{{highlight_green((1/2)(y-5)+y=38)}}}-----------continuing from here is no big chore.  Analyzing and forming this equation is the big chore.