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A basketball team won its first 8 games of the season, and then won 25

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A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 00:17
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A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24

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A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 00:28
Let the remaining games played by the basketball team be x

Since the team wins the first 8 games and 1/4rth of the remaining games, the equation framed it as follows :
\(\frac{8 + .25x}{8 + x} = \frac{1}{2}\)

\(16 + .5x = 8 + x\)

\(0.5x = 8\)
Multiplying by 2, \(x = 16\)

The total games played by the basketball team is 8+16 = 24(Option E)
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 01:04
Bunuel wrote:
A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24


Basketball team won its first \(8\) games of the season.

Let the remaining games be \(= x\)

Then won \(25\)% of its remaining games. \(=> 25\)% of \(x = \frac{25}{100} * x = \frac{1}{4}x\)

Total games played in season \(= 8 + x\)

Total games won \(= 8 + \frac{1}{4}x\) ---------- (i)

Team won \(50\)% of its games for the entire season. \(=> 50\)% of \((8 + x) = \frac{50}{100} * (8+x) = \frac{1}{2} (8+x)\) --------- (ii)

Equating (i) and (ii), we get;

\(8 + \frac{1}{4}x = \frac{1}{2} (8 + x) = \frac{1}{2} * 8 + \frac{1}{2}x\)

\(8 + \frac{1}{4}x = 4 + \frac{1}{2}x\)

\(\frac{1}{2}x - \frac{1}{4}x = 8 - 4\)

\(\frac{(2x-1x)}{4} = 4\)

\(\frac{1}{4}x = 4\)

\(x = 4*4 = 16\)

Total games played in season \(= 8 + x = 8 + 16 = 24\)

Answer (E)...
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 01:17
eqn :-

=> 8 + 1/4*(x-8)=1/2 * x

=> x = 24

x total number of games
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 11:38
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Bunuel wrote:
A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24


let t=total games
8+(t-8)/4=t/2
t=24
E
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 11 Aug 2017, 12:36
8+x/4/8+x=1/2
32+x/4/8+x=1/2
32+x/4(8+x)=1/2
32=2x
x=16
Answer=16+8=24=E
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 12 Aug 2017, 14:28
Bunuel wrote:
A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24


Let X = total games

8 + 1/4 (X - 8) = 1/2 X

8 + (1/4) X - 2= 1/2 X

1/4 X = 6...........X =24

Answer: E
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 28 Aug 2017, 22:19
8+x/4-2 = x/2
So X= 24
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 08 Sep 2017, 19:36
We can use answer choices as well.
Let us start from the middle.
Total games played is=18
50% won=9
First 8 games won then game left is 1 now this cannot be 25% of the rest of the 25% games won.
Let us take a higher no.
Let total no of games Played=24
50% of games won=12
first 8 games won left is 4.(Total games won is 12)
Rest of the games left is 16(24-8) and 25% of 16 is 4. Total games won -=8+4=12 Answer.
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Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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New post 08 May 2018, 09:19
I think this question can be solved by weighted averages.

Let the # of the remaining games be R then

8 + 1/4 (R) = 1/2 (R+8)

Solve for R.
After solving, R = 16
Total = R+8 = 16+8 = 24 = E
Re: A basketball team won its first 8 games of the season, and then won 25   [#permalink] 08 May 2018, 09:19
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