Question

2
21. Mallika has two flower beds in her garden. One beds has 18 rows of plants and
other has 24 rows of plants. Each of the beds has same numbers of plants. What
is the least number of plants in each flowerbeds?​

Answer 1

$\sf{\underline{\boxed{\purple{\large{\bold{ Solution}}}}}}$

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$\sf { \left[\begin{array}{cc}2x &x \\y &3y \end{array}\right] \: \: \left[\begin{array}{cc}3\\2\end{array}\right] = \left[\begin{array}{cc}16 \\9\end{array}\right]}$

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$\sf \left[\begin{array}{cc}2x\times 3 &x \times 2 \\y\times 3 &3y\times 2 \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

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$\sf \left[\begin{array}{cc}6x & +2x \\3y &+ 6y \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

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$\sf \left[\begin{array}{cc}8x \\ 9y \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

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Now ;

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8x = 16

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x = 16 / 8

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x = 2

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$\sf{\red{\boxed{\bold{x = 2 }}}}$

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9y = 9

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y = 9/ 9

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y = 1

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$\sf{\red{\boxed{\bold{y = 1}}}}$

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Answer 2

$\sf{\underline{\boxed{\purple{\large{\bold{ Solution}}}}}}$

⠀⠀⠀⠀

$\sf { \left[\begin{array}{cc}2x &x \\y &3y \end{array}\right] \: \: \left[\begin{array}{cc}3\\2\end{array}\right] = \left[\begin{array}{cc}16 \\9\end{array}\right]}$

⠀⠀⠀⠀

$\sf \left[\begin{array}{cc}2x\times 3 &x \times 2 \\y\times 3 &3y\times 2 \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

⠀⠀⠀⠀

$\sf \left[\begin{array}{cc}6x & +2x \\3y &+ 6y \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

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$\sf \left[\begin{array}{cc}8x \\ 9y \end{array}\right] \: \: = \left[\begin{array}{cc}16 \\9\end{array}\right]$

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Now ;

⠀⠀⠀⠀

8x = 16

⠀⠀⠀⠀

x = 16 / 8

⠀⠀⠀⠀

x = 2

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{x = 2 }}}}$

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9y = 9

⠀⠀⠀⠀

y = 9/ 9

⠀⠀⠀⠀

y = 1

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{y = 1}}}}$

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