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25 Sep 2020, 05:02
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Difficulty:
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80% (01:57) correct
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A basketball team has currently won 80% of its games. If the team wins half of its next 20 games, it will have won 60% of its games. How many games has the team played so far?
A. 8
B. 10
C. 15
D. 20
E. 32
A. 8
B. 10
C. 15
D. 20
E. 32
25 Sep 2020, 08:09
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We're mixing one group with an 80% average and another with a 50% ('half of its games') average, and arriving at an overall average of 60%. Using alligation:
--50---60------------80---
we can see that the overall average is closer to 50%, so not many games were played when the team was winning 80% of the time. Already the answer must be A or B. The ratio of the distances to the middle average on the number line above is 10 to 20, conveniently, so if 20 games were played when the team won 50% of its games, 10 must have been played when the team won 80% of its games.
You could also solve algebraically. If the team won 80% of x games, it won 0.8x games. It then won 10 out of 20 games. So in total it won 0.8x + 10 games, after playing x + 20 games. We know it won 60% of all of its games, so
(0.8x + 10)/(x + 20) = 60/100
8x + 100 = 6x + 120
2x = 20
x = 10
and since x is what we want to find, 10 is the answer.
--50---60------------80---
we can see that the overall average is closer to 50%, so not many games were played when the team was winning 80% of the time. Already the answer must be A or B. The ratio of the distances to the middle average on the number line above is 10 to 20, conveniently, so if 20 games were played when the team won 50% of its games, 10 must have been played when the team won 80% of its games.
You could also solve algebraically. If the team won 80% of x games, it won 0.8x games. It then won 10 out of 20 games. So in total it won 0.8x + 10 games, after playing x + 20 games. We know it won 60% of all of its games, so
(0.8x + 10)/(x + 20) = 60/100
8x + 100 = 6x + 120
2x = 20
x = 10
and since x is what we want to find, 10 is the answer.
Target4bschool
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25 Sep 2020, 23:23
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Suppose the team has played \(x\) games YET.
The team has won \(\frac{80}{100} *x\) games
Now, if team wins half of the 20 games, which is \(\frac{1}{2} * 20 =10\), it would have won 60% of the total games
So, if the team wins \(\frac{80}{100} * x + 10 \) games, it would be equal to 60% of the total number of games.
Total number of games = x (games played) + 20 (games remaining)
So, \(\frac{80}{100} * x + 10 = \frac{60}{100} * (x+20)\)
=>\(\frac{20}{100} * x = 12-10\)
=>x=10
Let me know if you have further questions.
The team has won \(\frac{80}{100} *x\) games
Now, if team wins half of the 20 games, which is \(\frac{1}{2} * 20 =10\), it would have won 60% of the total games
So, if the team wins \(\frac{80}{100} * x + 10 \) games, it would be equal to 60% of the total number of games.
Total number of games = x (games played) + 20 (games remaining)
So, \(\frac{80}{100} * x + 10 = \frac{60}{100} * (x+20)\)
=>\(\frac{20}{100} * x = 12-10\)
=>x=10
Let me know if you have further questions.
