If the Heat won 30% of their games in the first third of the season, what percent of their remaining games must they win to finish this season having won 50% of all their games?
A: 60 B: 70 C: 75 D: 80
2007-04-01 13:32:54 · 5 answers · asked by surfxaholic36 2 in Science & Mathematics ➔ Mathematics
30% of 1/3(Total Games) + X% of 2/3(Total Games) = 50% of Total Games.
.30 * TG/3 + X * 2TG/3 = .50 * TG
multiply both sides by 1/TG and TG is canceled out.
Notice how we don't even need to know how many games are in the season.
.30 * 1/3 + X * 2/3 = .50
.10 + 2/3 X = .50
X = 3/2(.50 - .10)
X = 1.5(.4)
X = .60
X = 60%
A: 60
2007-04-01 13:42:51 · answer #1 · answered by Thomas C 6 · 1⤊ 0⤋
There are 82 games in a regular season, so 82 / 3 = 27.3333 or 27 games. 27 x 30% = 8.1 or 8 games.
41 - 8 = 33 games to win.
82 - 27 = 55 games left.
33 / 55 = 60%
2007-04-01 20:41:52 · answer #2 · answered by drewbear_99 5 · 0⤊ 0⤋
If x = the total number of games, and p = percent of remaining 2/3 of the season,
.30(x/3) + p(2x/3) = .50x
.10x + 2px/3 = .50x subtract .10x from both
2px/3 = .40x mult both by 3
2px = 1.20x divide both by 2x
p = .60
2007-04-01 20:41:50 · answer #3 · answered by hayharbr 7 · 1⤊ 0⤋
the answer is A.
60 %
And the explanation is ...
So... If Heat is playing all the season 82 games (I think it is correct , but never mind, let it be 82, the final result is just the same) and Heat won 30% of their games of the first third of the season... that means they won exactly 8.19 games of 27.33...
Why?
27.33 is exactly one third of 82, and 8.19 is one third of them... (of 27.33)
So... If they already played 27.33 games then there is left 54.66 games of all 82. Because the firs third is gone and there is 2 thirds to go...
So... If Heat must to win 50% of the all 82 games than they must to win 41 game exactly... For the first third they won 8.19 games... And they must win overall 41 game to be 50%...
So... 41-8.19= 32.81 games left to must win...
8.19 games are already won and they must to win 32.81 to be 50%.... CLEAR...
So... 32.81 heat must to win of the remaining 54.66 games which are the two thirds of the remaining 82 games...
Simple calculation of 32.81/54.66=0.60025613 which give us aproximately 0.6 it is in percentages 60%
.... So... The answer is A and 60 percentages... i think it is clear.... You can calculate it easily with any number of Heats games... If they play 200 games (which is wrong) for the season the result is just the same...
2007-04-01 21:04:13 · answer #4 · answered by krtica78 1 · 0⤊ 1⤋
(1/3)*.30 + (2/3)x = .50
.10 + (2/3)x = .50
(2/3)x = .40
x = .40*3/2 = .60 = 60%
2007-04-01 20:42:12 · answer #5 · answered by Anonymous · 1⤊ 0⤋