A team has won 16 matcjes and lost 5 .if these matches represent 70% of the matches to be played. how many more matches should the team win so as to have a record of 80% wins?
0.7x = 21
x = 30 total matches
0.8 * 30 = _______ 80% wins
To solve this problem, we can set up a proportion based on the information given. Let's call the total number of matches to be played "x". We know that the team has won 16 matches, lost 5 matches, and these matches represent 70% of the total matches.
So, we can set up the following proportion:
(16 + 5) / x = 70 / 100
Adding the number of wins (16) and losses (5) gives us the total number of matches played so far, which is 21.
21 / x = 70 / 100
Next, we can cross-multiply to solve for x:
70 * 21 = 100 * x
x = (70 * 21) / 100
x = 14.7
Since we can't have a fraction of a match, we can round up the number of total matches to the next whole number. So, the total number of matches to be played is 15.
Now, the team wants to have a record of 80% wins. We can calculate how many more matches they need to win to achieve this.
Let's call the number of matches they need to win "y". We can set up the following proportion:
(16 + y) / 15 = 80 / 100
Cross-multiplying:
80 * 15 = 100 * (16 + y)
1200 = 1600 + 100y
100y = 1600 - 1200
100y = 400
y = 400 / 100
y = 4
Therefore, the team needs to win 4 more matches to have a record of 80% wins.