A number, one fourth of that number, and 1/5 of that number are added. The result is 58. What is the original number?



Answer :

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]