Question

I think of a number, halve it and subtract 1 from it. The result is double the amount obtained by dividing the number by 3 and subtracting 4 from it.

Answer 1

The number you are thinking is 42

refer to the attachment

Answer 2

$\huge\underline\mathfrak\red{Question:}$

I think of a number halve it and subtract 1 from it. The result is double the amount obtained by dividing the number by 3 and subtracting 4 from it. Find the number ?

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$\huge\underline\mathfrak\blue{Answer:}$

$\huge\underline\orange{X=42}$

$\sf\large\underline\pink{Thus \ the \ number \ you \ thought \ is : }$ $\huge\underline\mathfrak\orange{42}$

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$\huge\underline\mathfrak\green{Solution:}$

⇛$\rm\{let }$ the call the number you thought is x

⇛Then, if we halve it and subtract 1 from it, we get :

$( \frac{x}{2} ) - 1$

⇛If the result is double the amount obtained by dividing the number by 3 and subtracting 4 from it ,We get :

$2(( \frac{x}{3} ) - 4)$

⇛so, We have,

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

⇛Now, Distribute through 2 to the right hand side :

$( \frac{x}{2} ) - 1 = ( \frac{2}{3} )x - 8$

⇛now, Subtract $\frac{x}{2}$

from the both sides,

$- 1 = ( \frac{2}{3} )x - ( \frac{1}{2})x - 8$

⇛now, add 8 to the both sides,

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

⇛Now, we need to find a common denominator for the right hand side, which is 6.

⇛So ,transform each question:

$7 = ( \frac{4}{6} )x - ( \frac{3}{6})x$

$7 = ( \frac{1}{6} )x$

lastly,

⇛we divide both sides by $\frac{1}{6}$

which is same as multiplying both sides by $\frac{6}{1}$

so,

$x = 42$

$\sf\large\underline\pink{Thus \ the \ number \ you \ thought \ is : }$ $\huge\underline\mathfrak\orange{42}$

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hope it helps :))