Question

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 1

`\mathrm{Original \;number} = \boldsymbol{40}`

Explanation:

Let x be the original number
Then

one-fourth of x =
`{(1)/(4)x=(x)/(4)}`

one-fifth of that number =
`{(1)/(5)x=(x)/(5)}`

`x + (x)/(4)} + (x)/(5)} = 58`

Multiply throughout by 20

`20\cdot x + 20\cdot (x)/(4) + 20\cdot (x)/(5) = 20\cdot 58\\\\20x + 5x + 4x = 1160\\\\29x = 1160\\\\x = 1160/29 = 40\\\\\mathrm{Original number} = \boldsymbol{40}`