MHB What is 3/4 of the original number?

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The discussion revolves around solving the equation where a number is divided by three-quarters of itself, and the resulting quotient is multiplied by half of the original number to equal 64. By letting x represent the original number, the calculations show that x equals 96. Consequently, three-quarters of this number is calculated to be 72. Participants seek a more polished solution to the problem, with one providing a clearer mathematical representation of the steps involved. The final answer confirms that 3/4 of the original number is 72.
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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?
 
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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.
 
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

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

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