Find the positive number such that 1/2 of the number multiplied by 1/3 of the number, multiplied by 1/6 of the number
is equal to the number itself.
x/2 * x/3 * x/6 = x
x^3/36 = x
x^3 = 36x
x^2 = 36
x = 6
check:
3*2*1 = 6
To find the positive number, let's call it "x," we can set up an equation based on the given information.
We know that 1/2 of the number, multiplied by 1/3 of the number, multiplied by 1/6 of the number is equal to the number itself.
Mathematically, this can be expressed as:
(1/2) * (1/3) * (1/6) * x = x
To solve this equation, we can simplify the left side by multiplying the fractions:
(1/2) * (1/3) * (1/6) = 1/36
Now we can rewrite the equation as:
(1/36) * x = x
We can multiply both sides of the equation by 36 to eliminate the fraction:
36 * (1/36) * x = 36 * x
This simplifies to:
x = 36 * x
Next, we'll bring all the terms with x to one side of the equation:
x - 36 * x = 0
Applying the distributive property:
1 * x - 36 * x = 0
Simplifying further:
x - 36x = 0
Combining like terms:
-35x = 0
To solve for x, we divide both sides of the equation by -35:
x = 0 / -35
Therefore, the positive number that satisfies the given condition is x = 0.
Note: It is important to mention that in this case, the only value that satisfies the equation is 0.