find all the factors of 38,39 and 40. Do they have any factors in common? Explain how you can tell if some numbers have factors
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Answer:
91 people take Russian
26 people take French and Russian but not German
Step-by-step explanation:
To solve this problem, we must build the Venn's Diagram of this set.
I am going to say that:
-The set A represents the students that take French.
-The set B represents the students that take German
-The set C represents the students that take Russian.
We have that:
In which a is the number of students that take only Franch, A \cap B is the number of students that take both French and German , A \cap C is the number of students that take both French and Russian and A \cap B \cap C is the number of students that take French, German and Russian.
By the same logic, we have:
This diagram has the following subsets:
There are 155 people in my school. This means that:
The problem states that:
90 take Franch, so:
83 take German, so:
22 take French, Russian, and German, so:
42 take French and German, so:
41 take German and Russian, so:
22 take French as their only foreign language, so:
Solution:
(1) How many take Russian?
First we need to find , that is the number of students that take French and Russian but not German. For this, we have to go to the following equation:
.
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The number of students that take Russian is:
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Now we have to find c, that we can find in the equation that sums all the subsets:
For this, we have to find b, that is the number of students that take only German. Then we go to this eqaution:
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The number of people that take Russian is:
91 people take Russian
(2) How many take French and Russian but not German?
26 people take French and Russian but not German