If \( \frac{2}{3} \) of a number is 20 less than the original number, what is the original number?

Let the original number be \( x \). According to the problem, we have the equation: \[ \frac{2}{3}x = x - 20 \] To eliminate the fraction, we can multiply both sides of the equation by 3: \[ 3 \cdot \frac{2}{3}x = 3(x - 20) \] This simplifies to: \[ 2x = 3x - 60 \] Next, we can isolate \( x \) by subtracting \( 3x \) from both sides: \[ 2x - 3x = -60 \] This simplifies to: \[ -x = -60 \] Multiplying both sides by -1 gives: \[ x = 60 \] Thus, the original number is \[ \boxed{60} \] To verify, we can check if \( \frac{2}{3} \) of 60 is indeed 20 less than 60: Calculating \( \frac{2}{3} \times 60 \): \[ \frac{2}{3} \times 60 = 40 \] Now, checking if 40 is 20 less than 60: \[ 60 - 20 = 40 \] Since both sides match, our solution is confirmed. The original number is \[ \boxed{60} \]