A student played a computer game 500 times and won 370 of these games. He then won the next \( x \) games and lost none. He has now won \( 75 \% \) of the games he has played. Find the value of \( x \).

Let's denote the total number of games played now as \( 500 + x \) since the student played 500 games initially and then won \( x \) more games. The total wins are now \( 370 + x \). According to the information given, the student has won \( 75\% \) of all the games played: \[ \frac{370 + x}{500 + x} = 0.75 \] Now, we will solve this equation for \( x \). First, cross-multiply: \[ 370 + x = 0.75(500 + x) \] Now, distribute \( 0.75 \): \[ 370 + x = 375 + 0.75x \] Next, we will rearrange the equation by moving all terms involving \( x \) to one side and constants to the other: \[ x - 0.75x = 375 - 370 \] This simplifies to: \[ 0.25x = 5 \] Now, divide both sides by \( 0.25 \): \[ x = \frac{5}{0.25} = 20 \] Thus, the value of \( x \) is \[ \boxed{20} \]