Answer:
[tex]\mathrm{Original \;number} = \boldsymbol{40}[/tex]
Step-by-step explanation:
Let x be the original number
Then
one-fourth of x = [tex]{\dfrac{1}{4}x=\dfrac{x}{4}}[/tex]
one-fifth of that number = [tex]{\dfrac{1}{5}x=\dfrac{x}{5}}[/tex]
[tex]x + \dfrac{x}{4}} + \dfrac{x}{5}} = 58[/tex]
Multiply throughout by 20
[tex]20\cdot x + 20\cdot \dfrac{x}{4} + 20\cdot \dfrac{x}{5} = 20\cdot 58\\\\20x + 5x + 4x = 1160\\\\29x = 1160\\\\x = 1160/29 = 40\\\\\mathrm{Original number} = \boldsymbol{40}[/tex]
