Sharon, a tennis player, has won 54 out of 78 matches in her career. Find x, the number of matches she must win in a row to raise her win percentage to 75%

Question

 Solve for X

Answer 1

Let x = the number of consecutive wins

54 + x = the new number of wins

78 + x = the new number of games (since she is to have no losses going forward)

 

(54 + x)/(78 + x) = her new percentage of wins = .75 = 3/4

Cross multiply

216 + 4x = 234 + 3x

x = 18

 

Take this answer and make sure it satisfies the conditions of the problem.