Respuesta :
Answer:
Number was [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Let the number was x.
As per statement of the question,
Subtracted from [tex]6\frac{1}{4}[/tex]
⇒ [tex]6\frac{1}{4}[/tex] - x
⇒ [tex]\frac{25}{4}-x[/tex]
Difference was multiplied by [tex]1\frac{2}{3}[/tex]
= [tex](\frac{25}{4}-x)\times (1\frac{2}{3})[/tex]
= [tex](\frac{25}{4}-x)\times (\frac{5}{3})[/tex]
Then again multiplied by [tex]2\frac{4}{5}[/tex] Or [tex]\frac{14}{5}[/tex]
= [tex](\frac{25}{4}-x)\times (\frac{5}{3})\times (\frac{14}{5})[/tex]
= [tex](\frac{25}{4}-x)\times (\frac{14}{3})[/tex]
This result was same as the result of division of 146 by [tex]5\frac{3}{14}[/tex]
= [tex]\frac{146}{\frac{73}{14}}[/tex]
= [tex]\frac{146\times 14}{73}[/tex]
= 28
Now [tex](\frac{25}{4}-x)\times (\frac{14}{3})[/tex] = 28
[tex](\frac{25}{4}-x)=(\frac{3\times 28}{14})[/tex]
[tex](\frac{25}{4}-x)=6[/tex]
x = [tex]\frac{25}{4}-6[/tex]
= [tex]\frac{25-24}{4}[/tex]
= [tex]\frac{1}{4}[/tex]
= [tex]\frac{1}{4}[/tex]
