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-Everytime I formulate some data into an equation and solve it... It gives me wrong solution, for example: •In the battle of "Zama" (19 Oct. 202 BC) the Carthaginian army consisted of 36.000 infantrymen 4.000 knights (total: 40.000)

•Let the infantry be x the cavalry be y. Now, Let's suppose that I know only the half of cavalry numbers [ie. 2000 of 4000] and don't know the number of infantry. Finally, Let's formulate this into an equation

x+(y-2000)= 40.000

•When, Solving the equation x (number of infantry) equals 21.000 instead of the correct number which is 36.000 and y (number of knights) equals 19.000

What's the problem?!

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    You should write down an equation that says plainly "half of the calvary number $y$ is $2000$. There are two unknowns, but you only wrote down one equation (and it is wrong). – 2017-02-02

1 Answers 1

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If I understand correctly, you want to assume you know that there are $40000$ troops total, and that half of the calvary is $2000$. If this is the case, then you would have the system of equations: $$\begin{cases}x+y=40000\\\frac{y}{2}=2000\end{cases}$$ Where $x$ is the number of infantry and $y$ is the number of calvary. Simple substitution of the second equation into the first yields the result of $x=36000$.

The original equation you wrote is equivalent to saying that $x+y=42000$, which implies that there are $42000$ total troops.