Solving a problem situation in mathematics can be developed in several ways, as long as it is clear and achieves the expected result.
The same problem can be solved using the multiplication or addition operation or even different methods.
Equation is one of several ways to solve a mathematical problem. To apply this method of solving problem situations, it is necessary to follow some important steps:
• Remove important data to solve the problem.
• Identify what the unknown will be, that is, know what the problem wants to discover.
• Identify the operations involved.
• Assemble the equation.
• Solve the found equation, obtaining the unknown value.
• Check through the equation if the value (roots) found is correct.
See some problem situations solved through equations and how all the steps above were applied.
I thought of three consecutive numbers that add up to -72. What numbers did I think?
The only data the problem offered was:
- are three consecutive numbers.
- their sum is -72
Identification of the unknown:
First: he wants to find out what these three numbers are whose sum is -72.
We know for example that 2, 3, 4 are consecutive, because the number that comes after 2 is 2 + 1 = 3 and the other will be 2+2 = 4, following this line of reasoning we can say that:
Since we don't know the value of any of the three numbers we can call the first one x, so the next one would be x + 1 and the third one would be x + 2. So the sequence of numbers would look like this: x, x + 1, x + 2.
Identify the operation:
The operation will be addition, as he said the sum of these numbers is -72.
Assemble and solve the equation:
Now we add the sequence of numbers together and equal -72.
x + x + 1 + x + 2 = - 72
3x + 3 = - 72
3x = - 72 - 3
3x = - 75
x = - 75: 3
x = - 25
We find the value of x, so x + 1 = - 25 + 1 = - 24 and x + 2 = - 25 + 2 = - 23.
Therefore, the three consecutive numbers are: - 25, -24, - 23.
To check if the solution found is true, there are two ways:
1st way: the equation formed is x + x + 1 + x + 2 = - 72, as we found out the value of x, just replace it:
-25 + (-25) + 1 + (-25) + 2 = -72
-25 – 25 + 1 – 25 + 2 = - 72
- 72 = - 72
2nd way: as the sum of the three numbers must be -72 and we find the three, just add them up and check if their sum is really -72.
- 25 + (- 24) + (- 23) = -25 – 24 – 23 = -72.
by Danielle de Miranda
Graduated in Mathematics
Brazil School Team
Equation - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/equacoes-os-problemas-matematicos.htm