Question

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

Answer 1

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 $\frac{1}{4} x$, seven less than one-fourth of the number is $\frac{1}{4} x -7$. Two times the quantity of seven less than one-fourth of a number is therefore $2(\frac{1}{4} x -7)$.

One-third of the number is $\frac{1}{3} x$, four more than one-third of the number is given by $\frac{1}{3} x + 4$.

Step 2:

We substitute both equations to determine the value of x.

$2(\frac{1}{4} x -7) = \frac{1}{3} x + 4.$

$(\frac{2}{4} x -2(7)) = \frac{1}{3} x + 4.$

$\frac{1}{2} x -14 = \frac{1}{3} x + 4.$

$\frac{1}{2} x - \frac{1}{3} x = 4+14 = 18.$

$\frac{1}{6} x = 18.$

$x= 6(18) = 108.$

So the unknown number is 108.