Required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
" A number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the greater number
[tex]'y'[/tex] represents the smaller number
As per the given condition equation we have,
[tex]x- y = 44\frac{1}{2} \\\\\implies x-y = \frac{89}{2}[/tex] ______[tex](1)[/tex]
[tex]x-7y =10 \frac{3}{14} \\\\\implies x-7y = \frac{143}{14}[/tex] ______[tex](2)[/tex]
Subtract equation [tex](2)[/tex] from [tex](1)[/tex] to get the required numbers,
[tex]6y = \frac{89}{2} -\frac{143}{14} \\\\\implies 6y = \frac{623-143}{14}\\ \\\implies 6y = \frac{480}{14}\\ \\\implies y = \frac{40}{7}\\ \\\implies y = 5\frac{5}{7}[/tex]
Substitute the value of [tex]'y'[/tex] in [tex](1)[/tex] we get,
[tex]x= \frac{89}{2}+ \frac{40}{7} \\\\\implies x = \frac{623+80}{14} \\\\\implies x= \frac{703}{14}\\ \\\implies x= 50\frac{3}{14}[/tex]
Hence, required numbers as per the given condition are [tex]50\frac{3}{14}[/tex] and [tex]5\frac{5}{7}[/tex].
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