Let R=Roger's share then Sally's share is 60-R.
They each receive an extra $16, so Roger now has R+16 and Sally 76-R.
Roger has 10/13 of Sally's share so R+16=10(76-R)/13.
Therefore:
13(R+16)=10(76-R),
13R+208=760-10R,
23R=760-208=552, R, Roger's share=552/23=$24, so Sally's share is 60-24=$36.