Maths problem

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If 70% of the population speak English and 60% speak French, what percentage speak both?

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The way to understand this question is to ask the question with only 10 people.

If there are 10 people...

... and 7 of them speak English
... and 6 of them speak French

how many of them speak both?

One way to see this is by doing it out on paper with 'E' (for English speakers) and 'F's. With only 10 people you can quickly go through every possibility.

(It may be possible that there is more than one answer to this question).

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There's not enough information to answer. Perhaps 60% speak French and English, 10% speak English only, and the remaining 30% speak Spanish only.

Though you could logically derive the minimum percentage that must speak both languages for the statements to be true. Educational types really can be sloppy with their language and logic...

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I don't think it is sloppiness. I suspect the question is designed to show the solution is a set-- not a specific number.

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If you have 100 people:

70%...speak English----------> 70 people

60%...speak french------------->60 people

total English+french speakers--->130 people

But we have only 100 people to start with.

Thus, 130-100 = 30----> speak both English+ French

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And what of the mutes?!?!?

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Miller wrote:

If you have 100 people:

70%...speak English----------> 70 people

60%...speak french------------->60 people

total English+french speakers--->130 people

But we have only 100 people to start with.

Thus, 130-100 = 30----> speak both English+ French

No, Miller. That info would only be true if it was a given that everyone in the population spoke either English, French or both. This information is, however, not provided.

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You're reading too much into this story. It's simple.
The people are in 3 groups;

Group #1 speaks french
Group #2 speaks english
Group #3 speaks french + english

If we have only 100 people, but 70 speak english
and 60 speak french, it's apparent we have a surplus of 30 people (130-100 ) who speak both E and F.

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najmelliw wrote:

Miller wrote:
If you have 100 people:

70%...speak English----------> 70 people

60%...speak french------------->60 people

total English+french speakers--->130 people

But we have only 100 people to start with.

Thus, 130-100 = 30----> speak both English+ French

No, Miller. That info would only be true if it was a given that everyone in the population spoke either English, French or both. This information is, however, not provided.

And that info was NOT given because it wasn't needed. Much ado about nothing.

Laughing

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patiodog wrote:

And what of the mutes?!?!?

The mutes? Of course these people can either use sign language or have a translator at their side.

:wink: :wink: :wink:

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najmelliw wrote:

Miller wrote:
If you have 100 people:

70%...speak English----------> 70 people

60%...speak french------------->60 people

total English+french speakers--->130 people

But we have only 100 people to start with.

Thus, 130-100 = 30----> speak both English+ French

No, Miller. That info would only be true if it was a given that everyone in the population spoke either English, French or both. This information is, however, not provided.

Maths problem

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