Carcass wrote:
A soccer team won 10 games and lost 5 games. If the team wins the next k games, it will have won 75 percent of all the games played. What is the value of k?
Given: The team has won 10 games and lost 5 gamesSo, the team has played a total of
15 games so far.
If the team wins the next k games, then:
The total number of games won =
10 + kThe total number of games played =
15 + kWe can write: (
10 + k)/(
15 + k)
= 75/100 (aka 75%)
Simplify the right side: : (
10 + k)/(
15 + k)
= 3/4Cross multiply:
4(10 + k) = 3(15 + k)Expand:
40 + 4k = 45 + 3kSolve:
k = 5Answer: 5