The unknown number is 108.
Step-by-step explanation:
Step 1:
Assume the unknown number is x.
We create an equation from the given data.
One-fourth of the number is [tex]\frac{1}{4} x[/tex], seven less than one-fourth of the number is [tex]\frac{1}{4} x -7[/tex]. Two times the quantity of seven less than one-fourth of a number is therefore [tex]2(\frac{1}{4} x -7)[/tex].
One-third of the number is [tex]\frac{1}{3} x[/tex], four more than one-third of the number is given by [tex]\frac{1}{3} x + 4[/tex].
Step 2:
We substitute both equations to determine the value of x.
[tex]2(\frac{1}{4} x -7) = \frac{1}{3} x + 4.[/tex]
[tex](\frac{2}{4} x -2(7)) = \frac{1}{3} x + 4.[/tex]
[tex]\frac{1}{2} x -14 = \frac{1}{3} x + 4.[/tex]
[tex]\frac{1}{2} x - \frac{1}{3} x = 4+14 = 18.[/tex]
[tex]\frac{1}{6} x = 18.[/tex]
[tex]x= 6(18) = 108.[/tex]
So the unknown number is 108.
