Question 1203977
The account which gained 6.7%, y quantity invested
The account which lost 7.8%, 10000-y quantity invested


Starting total quantity was  10000 dollars.  (Assuming you made typing mistake)
Ending quantity was {{{10000-562.5}}} dollars, or 9437.5 dollars.


Forming the equation by description:
{{{y+0.067y+(10000-y)-(10000-y)0.078=9437.5}}}--------first, think how this makes sense; and then when you are satisfied, solve for y.