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?

probability combinatorics permutations combinations percentages

2,100

Solution 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.

Solution 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 $x+5$.

2,100

sy254191

Updated on August 01, 2022

Comments

sy254191 over 1 year

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
- paw88789 about 5 years
  
  Was there no punctuation in the problem?
- sy254191 about 5 years
  
  i edit the question plz check again
- callculus42 about 5 years
  
  @sy254191 You´ve got several answers plz give a reply.
- sy254191 about 5 years
  
  @callculus I think farruhota answers is correct
- callculus42 about 5 years
  
  @sy254191 Sure, as well as my answer.
- sy254191 about 5 years
  
  @callculus yes your answer also.
GoodDeeds about 5 years

I believe the OP only asked for an explanation of the question.
callculus42 about 5 years

Please check your result.
sy254191 about 5 years

the options are: A)14 B)25 C)16 D)20
sy254191 about 5 years

the options are: A)14 B)25 C)16 D)20
sy254191 about 5 years

i edit the question plz check again
GoodDeeds about 5 years

@sy254191 Did you try solving the problem yourself? I have tried explaining what the question asks for in my answer, which was your question. I suggest you attempt it yourself first.
GoodDeeds about 5 years

This answer is wrong. After playing five more games, the win percentage is 70%, not 75%. $x=5$ does not satisfy the equation you have written.
callculus42 about 5 years

@sy254191 The solution is $l+w+5=20$. This is the number of games the team played overall. Solve the first equation for $w$ to obtain $w=4l$. The insert the expression for $w$ into the second equation: $\frac{l+2}{l+4l+5}=0.25$. Now solve the equation for $l$.
prog_SAHIL about 5 years

@GoodDeeds, Sorry it was $15$. I miscalculated in a hurry.
prog_SAHIL about 5 years

@callculus, Edited.