Computational problems are direct and indirect.
Here is an example of the direct problem: what is the weight of a piece of alloy, the manufacture of which went 0.6 dm3 copper (density 8.9 kg/dm3) and 0.4 dm3 zinc (density 7.0 kg/dm3)?
Under the decision taken is a lot of copper (8.9 · 0.6 = 5.34 kg), then the mass of zinc (7.0 · 0.4 = 2.8 kg), and finally, the mass of the alloy (5.34 + 2.8 = 8.14 kg). Your actions and their sequence dictated by the condition of the problem.
Here is an example of indirect tasks: a piece of alloy of copper and zinc volume of 1 dm3 weighs 8.14 kg. Find the volume of copper and zinc in the alloy. Here, from the condition of the problem is not clear what actions will lead to a solution. In the so-called arithmetic solutions often need to show great ingenuity to outline plan to solve the problem indirectly. Each new challenge requires a new plan. Labor calculator spent inefficiently. To streamline the process, and the computational method was created equations, which is the main subject of study in algebra. The essence of this method is as follows. Learn more about algebra help.
Unknown quantities are marked. We use for this purpose alphabetic characters (preferably the latest lowercase Roman letters x, y, z, u, v). Condition problem with these marks and action (+, -, etc.) “is translated into the language of mathematics” that is, the relationship between the data and the unknown quantities, we express no words and phrases in spoken language, and mathematical signs. Each such “mathematical sentence” is the equation.
After that, we solve the equation, that is, find the values of the unknown unknowns. Solution of the equation is quite mechanically, by common rules. We do not have to take more account of features of this problem, we only have to apply once the rules and techniques. (The output of these rules and engaged primarily in algebra.)
Thus, the equations need to mechanize the work of the calculator. When the equation is made, its solution can be completely automatic. The whole difficulty of solving the problem reduces to the equations.