The difference between the number of people who speak French and Spanish is 15,637,000 and the difference between those who speak French and German is 155,000, while the total number of people who speak all three is 20,588,000. Determine from information the number of people who speak each language.
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To determine the number of people who speak each language, we can use a method called Venn diagram. Let's break down the given information step by step:
1. The difference between the number of people who speak French (F) and Spanish (S) is 15,637,000. This means that the number of people who speak French but not Spanish (F-S) is 15,637,000.
2. The difference between the number of people who speak French (F) and German (G) is 155,000. This implies that the number of people who speak French but not German (F-G) is 155,000.
3. The total number of people who speak all three languages (French, Spanish, and German) is 20,588,000.
Now, let's use this information to find the number of people who speak each language:
1. To find the number of people who speak French, we need to calculate the sum of those who speak only French (F-S) and those who speak both French and Spanish (F ∩ S) and those who speak both French and German (F ∩ G) and those who speak all three languages (F ∩ S ∩ G):
F = (F-S) + (F ∩ S) + (F ∩ G) + (F ∩ S ∩ G)
2. We know that the number of people who speak all three languages (F ∩ S ∩ G) is 20,588,000. So, we can substitute this value into the equation:
F = (F-S) + (F ∩ S) + (F ∩ G) + 20,588,000
3. Now we can substitute the given differences between the number of people who speak French and Spanish (F-S = 15,637,000) and between French and German (F-G = 155,000):
F = 15,637,000 + (F ∩ S) + 155,000 + 20,588,000
4. Simplifying the equation:
F = 36,380,000 + (F ∩ S)
5. Now let's find the value of (F ∩ S) - the number of people who speak both French and Spanish:
(F ∩ S) = F - (F-S)
(F ∩ S) = F - 15,637,000
6. Substitute this value back into the equation:
F = 36,380,000 + (F - 15,637,000)
7. Simplifying further:
F = 20,743,000
So, the number of people who speak French (F) is 20,743,000.
To find the number of people who speak Spanish (S):
S = F - (F-S)
S = 20,743,000 - 15,637,000
S = 5,106,000
Therefore, the number of people who speak Spanish (S) is 5,106,000.
To find the number of people who speak German (G):
G = F - (F-G)
G = 20,743,000 - 155,000
G = 20,588,000
Therefore, the number of people who speak German (G) is 20,588,000.
In summary:
- The number of people who speak French is 20,743,000.
- The number of people who speak Spanish is 5,106,000.
- The number of people who speak German is 20,588,000.