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If $d-6c=4$ and $2d-9c=20$, find the value of $\frac{d}{c}$.

Jul 24, 2021

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If

$$d-6c=4$$ and $$2d-9c=20$$, find the value of $$\dfrac{d}{c}$$.

$$\begin{array}{|rcll|} \hline 2d-9c &=& 20 \quad | \quad :c \\\\ \mathbf{\dfrac{2d}{c}-9} &=& \mathbf{\dfrac{20}{c}} \qquad (1) \\ \hline \end{array} \begin{array}{|rcll|} \hline d-6c &=& 4 \quad | \quad :c \\\\ \dfrac{d}{c}-6 &=& \dfrac{4}{c} \quad | \quad *5 \\\\ \mathbf{\dfrac{5d}{c}-30} &=& \mathbf{\dfrac{20}{c}} \qquad (2) \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline (2)=(1): & \dfrac{5d}{c}-30 &=& \dfrac{2d}{c}-9 \\\\ & \dfrac{3d}{c} &=& 30 -9 \\\\ & \dfrac{3d}{c} &=& 21 \quad | \quad :3 \\\\ & \mathbf{\dfrac{d}{c}} &=& \mathbf{7} \\ \hline \end{array}$$

Jul 24, 2021