Question

When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the number? Express your answer as a common fraction. When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the number? Express your answer as a common fraction. @Mathematics

Answer 1

a*(2a+1/2a)=a

Answer 2

Let x denote the number we're looking for. From the problem,
\[ x * (2x + \frac{x}{2}) = x \]
So we have that
\[2x^2 + \frac{x^2}{2} = x \rightarrow \frac{4x^2}{2}+\frac{x^2}{2} = \frac{5x^2}{2} = x\]
since we're given that x must be positive, we know it can't be zero. Therefore, it's safe to divide by x, and we find that
\[ \frac{5x}{2} = 1 \rightarrow x = \frac{2}{5} \]
Note that, if we didn't have the restriction that x must be positive, zero would work just as well.

Answer 3

Simplify it by showing that

a(5/2a)=a

5/2a=1

a=2/5