Solution:

14 hits in the last 10 games
.467 average over the last 10 games

Currently Johnny has 30 at-bats and 10 hits (.333 x 30 at-bats = 10 hits or 10 hits/30 at-bats = .333 average). If Johnny gets 3 at-bats per game over the last 10 games of the season, he will have 30 more at-bats or a total of 60 at-bats for the season. To hit .400 for the season, Johnny would need 24 hits (.400 x 60 at-bats = 24 hits or 24 hits/60 at-bats = .400 average). Since he already has 10 hits, he needs another 14 hits in his last 30 at-bats to reach 24 hits for the season. 14 hits in 30 at-bats will give him a .467 average over the last 10 games (14 hits/30 at-bats = .467 average)