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→x+15=35→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.
