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 \( x \).

To find the value of \( x \), we can follow these steps: 1. **Identify the known values:** - The student played 500 games and won 370 of them. - He won \( x \) additional games and lost none. - After winning \( x \) games, he has won \( 75\% \) of all the games he has played. 2. **Set up the equation:** - The total number of games played after winning \( x \) more games is \( 500 + x \). - The total number of games won after winning \( x \) more games is \( 370 + x \). - According to the problem, the student has won \( 75\% \) of the total games played, which can be expressed as: \[ \frac{370 + x}{500 + x} = 0.75 \] 3. **Cross-multiply to eliminate the fraction:** \[ 370 + x = 0.75(500 + x) \] 4. **Distribute \( 0.75 \):** \[ 370 + x = 375 + 0.75x \] 5. **Rearrange the equation to isolate \( x \):** \[ 370 + x - 0.75x = 375 \] \[ 370 + 0.25x = 375 \] \[ 0.25x = 375 - 370 \] \[ 0.25x = 5 \] 6. **Solve for \( x \):** \[ x = \frac{5}{0.25} = 20 \] Thus, the value of \( x \) is \( 20 \). The student won 20 additional games.