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

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

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11 Aug 2017, 00:17
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25% (medium)

Question Stats:

81% (01:05) correct 19% (01:16) wrong based on 143 sessions

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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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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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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 $$= 8 + x = 8 + 16 = 24$$

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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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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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Joined: 07 Dec 2014
Posts: 1032
Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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11 Aug 2017, 11:38
1
1
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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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
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Joined: 26 Mar 2013
Posts: 1718
Re: A basketball team won its first 8 games of the season, and then won 25 [#permalink]

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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

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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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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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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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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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