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Answer :
Final answer:
To achieve a 90% winning percentage, the tennis team needs to win 30 more games in a row, as calculated from the equation (15 + x) / (20 + x) = 0.9, where x is the number of additional wins needed.
Explanation:
The question is asking how many consecutive wins are needed for a tennis team to achieve a winning percentage of 90%. The team has won 15 out of 20 matches. To reach a 90% winning percentage, which is equivalent to winning 9 out of every 10 games, we need to determine the total number of games (both played and to be played) that will result in a 90% winning ratio.
Let's denote the number of additional wins required by x. Therefore, the team would have won 15 + x matches out of 20 + x total matches. To find x, we set up the equation (15 + x) / (20 + x) = 0.9 and solve for x.
Here is the step-by-step calculation:
Multiply both sides of the equation by (20 + x) to get rid of the denominator: 15 + x = 0.9 * (20 + x).
Expand the right side: 15 + x = 18 + 0.9x.
Subtract 0.9x from both sides: 0.1x = 3.
Divide both sides by 0.1 to find x: x = 30.
The team needs to win 30 more games in a row to have a 90% winning percentage.
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Answer:
Step-by-step explanation:
You see, 15/20 = 75%... 75% = 75/100. So, (15 + t)/(20 + t) = 90%... 90% = 90/100. Solve for (t).
(15 + t)/(20 + t) = 90/100
90(20 + t) = 100(15 + t)
1800 + 90t = 1500 + 100t
10t = 300
t = 30 matches
The team would have to win 30 more matches in a row (that's 45 out of 50 matches).
