in a class of 40 students,60% speak french and 50% speak english how many student speak both languages?
60% + 50% = over 100% so you know that 60 over laps 50, but by how much? 10 percent
now that you know how much percent does both, find out the number.
What is 60% of 40?
24
What is 50% of 40?
20
What is 10% of 40?
4
4 students speak both languages
Restating:
60% of the 40 speak French or 24 speak French
50% of the 40 speak English or 20 speak English
x students of the 40 speak both languages, so
24-x + x + 20-x = 40
solve for x
Verify your answer with a Venn diagram
In a class of 40 students, 60% speak french and 50% speak English.How many students speak both languages? 1 .In a Venn diagram.
To solve the problem using a Venn diagram:
1. Draw two overlapping circles representing French and English speakers.
2. Label the left circle "French" and the right circle "English".
3. Write "40" in the center (this represents the total number of students in the class).
4. Since 60% speak French, shade in 60% of the "French" circle (24 students).
5. Since 50% speak English, shade in 50% of the "English" circle (20 students).
6. The students in the overlap of the circles represent those who speak both languages.
7. To find the number of students who speak both languages, count the shaded area in the overlap section.
8. The shaded area in the overlap section represents 4 students who speak both languages.
Therefore, 4 students speak both French and English.
To find out how many students speak both French and English, we need to determine the overlap between the two groups.
Step-by-step solution:
1. Calculate the number of students who speak French: Multiply the total number of students by the percentage (60% = 0.6):
Number of students who speak French = 40 * 0.6 = 24.
2. Calculate the number of students who speak English: Multiply the total number of students by the percentage (50% = 0.5):
Number of students who speak English = 40 * 0.5 = 20.
3. Find the overlap by using the concept of sets. The total number of students who speak both French and English is equivalent to the intersection of the sets of students who speak French and English.
Intersection = Number of students who speak French + Number of students who speak English - Total number of students (40) as it represents double counting.
Intersection = 24 + 20 - 40 = 4.
Therefore, 4 students speak both French and English.