OG - PS - #165

[MWW7786]

Hey again. I hope this message finds you well. :cool:

I read the solution in the OG on math prob. #165; the explanation was logical. I need to be able to do this kind of problem the MGMAT way, so I'll recognize on the test. Can you please throw some light on this?

#165
During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of entire games during the year, what was the total of games played?

a. 180
b.170
c.156
d.150
e.105


d is correct
solution: equation .80(100)+.50(x-100)=.70x
Can we set this up with the box diagrams?

[StaceyKoprince]

Hey - not entirely sure what you mean by "box diagrams" - are you talking about either overlapping sets or clicking charts?

In any case, this problem is a weighted average problem - they have been popping up more frequently lately as a harder average problem, so good to know how to handle it.

The idea is that, normally, when we take an average, we just average whatever two numbers we're dealing with. That actually assumes that the two items are equally weighted, or contribute equally to the final result. So, if I say one person weighs 130 and another weighs 145, if I want to calculate the average, I assume that both people contribute equally to that calculation.

In the given problem, though, the two values we're dealing with are unbalanced (because the two percentages represent different numbers of games).

So instead of thinking about averaging, think about calculating the specific numbers you're dealing with and just walk your way through it.

They won 80% of the first 100 games, so that's 80 games. They won 50% of the remaining games, so that's .50x (since I don't know the number of games). Finally, they won 70% of ALL of the games, so that's .70(100+x). (Notice that the equation I'm writing is slightly different than the one given by OG).

# they won out of first 100 + # they won out of remaining = total # won
80 + 0.5x = 0.7(100+x)
Now it's just a matter of solving for x.