Middle School

A tennis team has won 15 out of 20 matches they have played this season. How many more matches will they have to win in a row to raise their winning percentage to 90%?

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.

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).