April 4, 2021 1 min to read

Fisherman and the golden fish - Ratio

Ông lão đánh cá và con cá vàng - Bài toán tỉ lệ

• System of equations

  on the theory about systems of equations, please refer to this game .

• General Theory

  given the system of equation \[\begin{cases}a \times x + b\times y=c \\ \frac{x}{y}=d \end{cases}\], Denote the first equation as (1), and the second equation as (2).

  Then from (2), we have \(x=\frac{d}{y}\). Swap \(x\) for \(\frac{d}{y}\) in (1), we have a quadratic equation of variable y.

  Now if you are primary schooler and have not been able to solve quadratic equations, then the given \(d\) should also be rational and \(d=\frac{e}{f}\).

  Then, in (1), swap \(x\) for \(ez\), \(y\) for \(fz\). We shall have an easy equation for variable \(z\).

  Remember to find \(x\) and \(y\), don't stop after you find \(z\)!

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