algebraic and mental method for resolving this problem
Please show me how to arrive at the correct answer (40%) to this question using mental arithmetic AND algebra
In a town, 80% of the population speak English and 60% of the population speak Gaelic.
What percentage of the population speak both languages ?
In a town, 80% of the population speak English and 60% of the population speak Gaelic.
What percentage of the population speak both languages ?
d-glitch
You just have to add the two numbers and subtract 100.
That assumes that 100% of the people in the town speak English or Gaelic or both.
Is a non-negligible and unknown percentage speak only French or are mute then you can not solve the problem.
Venn Diagrams also work for these sort of problems.
Is a non-negligible and unknown percentage speak only French or are mute then you can not solve the problem.
Venn Diagrams also work for these sort of problems.
ASKER
> That assumes that 100% of the people in the town speak English or Gaelic or both.
This is a correct asumption
> You just have to add the two numbers and subtract 100.
I can see that that gives the correct solution, but I can't quite see the logic.
Algebraic solution anyone ?
This is a correct asumption
> You just have to add the two numbers and subtract 100.
I can see that that gives the correct solution, but I can't quite see the logic.
Algebraic solution anyone ?
ASKER CERTIFIED SOLUTION
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SOLUTION
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SOLUTION
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>> SuperDave
There is no range.
In this problem exactly 60 people/percent speak both languages.
And you can also calculate that (80-40) ==> 40 people speak only English and (60-40) ==> 20 people speak only Gaelic.
There is no range.
In this problem exactly 60 people/percent speak both languages.
And you can also calculate that (80-40) ==> 40 people speak only English and (60-40) ==> 20 people speak only Gaelic.
There is no range.
In this problem exactly 40 people/percent speak both languages.
And you can also calculate that (80-40) ==> 40 people speak only English and (60-40) ==> 20 people speak only Gaelic.
In this problem exactly 40 people/percent speak both languages.
And you can also calculate that (80-40) ==> 40 people speak only English and (60-40) ==> 20 people speak only Gaelic.
SOLUTION
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E = English only
G = Gaelic only
B = Both
E + G + B = 100
E + B = 80 ==> Three equations in three unknowns.
G + B = 60
d-glitch: It's not stated in the problem that everybody speaks English or Gaelic or both. The 20% range is the people who speak neither, so if you want to add the restriction that that's 0%, then you get the 40% speaking both.
>> >> That assumes that 100% of the people in the town speak English or Gaelic or both.
This is a correct asumption
This was added later.
This is a correct asumption
This was added later.
E = English only
G = Gaelic only
B = Both
N = Neither
E + G + B + N = 100
E + B = 80 ==> Three equations in four unknowns.
G + B = 60 You don't have enough information to find a solution.ASKER
This was an interesting question and the answers were intriguing. Well done d-glitch on coming up with a double-barelled solution.
Thanks all ... now go and pose it to your friends !
Thanks all ... now go and pose it to your friends !
ASKER
Sorry, It was wEdmorho o came up with the second method
If all of the 60% who speak Gaelic also speak English, then 60% of the population speaks both. (20% speak neither.)
If the 20% that does not speak English do speak Gaelic, then 40% speak both.
We do not know if a third language is involved. If it becomes known that there is no third language, then the answer is 40%.
If there is a third (or more) language, things get uncertain. We know from the question that there must be some that speak both, but we can only be certain for now that the range is from 40% to 60%. The two known languages cannot overlap more than 60% nor less than 40%.
Tom
If the 20% that does not speak English do speak Gaelic, then 40% speak both.
We do not know if a third language is involved. If it becomes known that there is no third language, then the answer is 40%.
If there is a third (or more) language, things get uncertain. We know from the question that there must be some that speak both, but we can only be certain for now that the range is from 40% to 60%. The two known languages cannot overlap more than 60% nor less than 40%.
Tom