# How many of each calculator was sold if a simple calculator costs $5 and scientific calculator costs$16 and the store sold 35 calculators for total amount of $340? ##### 1 Answer Feb 6, 2015 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:
$x + y = 35$
$5 x + 16 y = 340$
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 $y$:
$5 x + 16 y = 5 \left(35 - y\right) + 16 y = 175 - 5 y + 16 y$, from which we obtain
$175 + 11 y = 340$.
Subtracting $175$ from both sides, we get
$11 y = 165$
which yelds, dividing by $11$ both members,
$y = 15$.

Since $y$ is now known, from the first equation we easily compute
$x + y = 35 \setminus \rightarrow x + 15 = 35 \setminus \rightarrow x = 20$.

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 $100 + 240 = 340$.