A team won 80% of the games it played 5 more games of which it won 3 and lost 2. Its loss percentage changed to 25% how many games it play overall?

Question

A team won 80% of the games it played 5 more games of which it won 3 and lost 2. Its loss percentage changed to 25% how many games it play overall ?

What does this question mean? I am not able to understand!
the options are:

A)14

B)25

C)16

D)20

Answer 1

A team won 80% of the games it played 5 more games of which it won 3 and lost 2. Its loss percentage changed to 25% how many games it play overall? A)14 B)25 C)16 D)20.

Since the answer choices for overall number of games are given, you can try them.

The first condition states "a team won $80\%$ of the games".

A) $(14-5)\cdot 0.8=7.2$ (impossible);

B) $(25-5)\cdot 0.8=\color{blue}{20}\cdot 0.8=\color{green}{16}$ (possible); it implies the team lost $\color{blue}{20}-\color{green}{16}=\color{red}4$ games, which makes $\frac{4}{20}=20\%$;

C) $(16-5)\cdot 0.8=8.8$ (impossible);

D) $(20-5)\cdot 0.8=\color{blue}{15}\cdot 0.8=\color{green}{12}$ (possible); it implies the team lost $\color{blue}{15}-\color{green}{12}=\color{red}3$ games, which makes $\frac{3}{15}=20\%$.

Hence, the options A and C are eliminated.

The second condition states: "its loss percentage changed to $25\%$".

B) out of total $20+5=25$ games, the team lost $4+2=6$ games, which makes $\frac6{25}=24\%$. So, the loss percentage changed from $20\%$ to $24\%$. (does not match)

D) out of total $20+5=25$ games, the team lost $3+2=5$ games, which makes $\frac5{25}=25\%$. So, the loss percentage changed from $20\%$ to $25\%$. (does match)

Hence, the answer is D.

Now you can think of making up equations and solving.

Answer 2

Suppose the team initially played $x$ number of games. The problem states that it won $80\%$ of these $x$ games.

Then, the team played five more games, which gives a total of $x+5$ games. Of these new five games, it won three and lost two. By doing so, its loss percentage changed to $25\%$, i.e., its win percentage is down to $75\%$ from $80\%$.

Given these conditions, the problem is to find $x+5$.

Answer 3

Assume they played $x$ games before the match.

As there win $\%$age is $80%$ they won $0.8x$ games and lost the rest i.e. $0.2x$ games.

After playing $5$ more games they lost $2$ and there loss $\%$age became $25$%.

This can be written as,

$$\frac{\text{Total lost games}}{\text{Total games played}}\cdot100=25$$

$$\frac{0.2x+2}{x+5}=.25$$

$$x=15$$

So they played $20$ games in total.

Answer 4

A team won 80% of the games

That means that the team played $x$ number of games of which the team won 80%.

If we denote $l$ for the number of lost games and $w$ for the number of won games, then the equation is

$$\frac{w}{l+w}=0.8$$

It played 5 more games of which it won 3 and lot 2 its loss % changed to 25%

Then the team played 5 additional games of which 3 games were won and 2 games were lost. In total $25\%$ of the games were lost. The corresponding equation is

$$\frac{l+2}{(l+3)+(w+2)}=\frac{l+2}{l+w+5}=0.25$$