This problem is easy to solve, once you write it in a proper notation. Let #x# be the number of simple calculators sold, and #y# be the number of scientific calculators sold. Knowing that a total of #35# calculators have been sold, means that #x+y=35#.
Moreover, if any simple calculator was sold at #$5#, and any scientific calculator was sold at #$16#, for a total income of #$340#, this means that #x*$5 + y* $16=340#. In fact, this equation says that the number of calculators sold times their price equals the total income.
Putting the two things together, we have the following system:
#x+y=35#
#5x+16y=340#
The system can be solved in many ways, one of which is substitution: from the first equation, we have that #x=35-y#. Plugging this identity in the second equation, we can calculate #y#:
#5x+16y=5(35-y)+16y=175-5y+16y#, from which we obtain
#175+11y=340#.
Subtracting #175# from both sides, we get
#11y=165#
which yelds, dividing by #11# both members,
#y=15#.
Since #y# is now known, from the first equation we easily compute
#x+y=35 \rightarrow x+15=35 \rightarrow x=20#.
You can verify the result: #20# simple calculators sold at #$5# each produce an income of #20*$5=$100#. #15# scientific calculators sold at #$16# each produce an income of #15*$16=$240#. Adding the two, we have #100+240=340#.
