Question

Two times the quantity of seven less than one-fourth of a number is equal to fout

more than one-third of the number. What is the number?​

Answer 1

The unknown number is 108.

Explanation:

Step 1:

Assume the unknown number is x.

We create an equation from the given data.

One-fourth of the number is
`(1)/(4) x`, seven less than one-fourth of the number is
`(1)/(4) x -7`. Two times the quantity of seven less than one-fourth of a number is therefore
`2((1)/(4) x -7)`.

One-third of the number is
`(1)/(3) x`, four more than one-third of the number is given by
`(1)/(3) x + 4`.

Step 2:

We substitute both equations to determine the value of x.

`2((1)/(4) x -7) = (1)/(3) x + 4.`

`((2)/(4) x -2(7)) = (1)/(3) x + 4.`

`(1)/(2) x -14 = (1)/(3) x + 4.`

`(1)/(2) x - (1)/(3) x = 4+14 = 18.`

`(1)/(6) x = 18.`

`x= 6(18) = 108.`

So the unknown number is 108.