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In the first half of last year, a team won 60 percent of the
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05 Mar 2017, 09:11
05 Mar 2017, 09:11
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Question Stats:
61% (02:12) correct
38% (02:16) wrong based on 246 sessions
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In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?
A) 60
B) 70
C) 80
D) 90
E) 100
A) 60
B) 70
C) 80
D) 90
E) 100
Re: In the first half of last year, a team won 60 percent of the
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11 Mar 2017, 20:13
11 Mar 2017, 20:13
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Explanation
Total games last year = \(x\)
Games in 2nd half of year = \(20\)
Games in 1st half of year = \(x - 20\)
60% of games in first half + 3 games in second half = 50% of the total games
\(0.60 \times (x - 20) + 3 = 0.50 \times x\)
\(0.60(x - 20) + 3 = 0.50x\)
\(0.60x - 12 + 3 = 0.50x\)
\(0.60x - 9 = 0.50x\)
\(-9 = -0.10x\)
\(x =90\)
Hence option D is correct.
Total games last year = \(x\)
Games in 2nd half of year = \(20\)
Games in 1st half of year = \(x - 20\)
60% of games in first half + 3 games in second half = 50% of the total games
\(0.60 \times (x - 20) + 3 = 0.50 \times x\)
\(0.60(x - 20) + 3 = 0.50x\)
\(0.60x - 12 + 3 = 0.50x\)
\(0.60x - 9 = 0.50x\)
\(-9 = -0.10x\)
\(x =90\)
Hence option D is correct.
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Re: In the first half of last year, a team won 60 percent of the
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21 Sep 2018, 05:46
21 Sep 2018, 05:46
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Carcass wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?
A) 60
B) 70
C) 80
D) 90
E) 100
Let T = TOTAL number of games played last year
The team won 50 percent of the games it played last year
So, TOTAL NUMBER OF WINS = 0.5T
In the SECOND HALF of last year, the team played 20 games, winning 3 of them
Number of WINS IN SECOND HALF = 3
If the team plays 20 games in the SECOND HALF, then T - 20 = the number of games played in the FIRST HALF
In the first half of last year, a team won 60 percent of the games it played.
So, the team won 60% of the T - 20 games it played in the FIRST HALF
Number of WINS IN FIRST HALF = (0.6)(T - 20)
We know that: WINS IN FIRST HALF + WINS IN SECOND HALF = TOTAL NUMBER OF WINS
So: (0.6)(T - 20) + 3 = 0.5T
Expand: 0.6T - 12 + 3 = 0.5T
Simplify left side: 0.6T - 9 = 0.5T
Subtract 0.6T from both sides to get: -9 = -0.1T
Solve: T = 90
Answer: D
Cheers,
Brent
i made it 
