What is 3/4 of the original number?

[Marcelo Arevalo]

A number is divided by 3/4 of it. Then the quotient is multiplied by half of the original number. The product equals 64. What is 3/4 of the number?

 

[Marcelo Arevalo]

Let x be the number
x / 0.75x = 1 1/3 X
Then 1 1/3 X (1/2X) = 2/3X
and 2/3 X must be = 64
so x = 96

wht is 3/4 of 96? = 72

can anyone help me construct a more polished solution?
thank you.

 

[MarkFL]

I would write:

$$x\cdot\frac{4}{3x}\cdot\frac{1}{2}x=64$$

$$\frac{2}{3}x=64\implies x=3\cdot32=96$$

Hence

$$\frac{3}{4}x=\frac{3}{4}96=3\cdot24=72$$