In a class, the number of students that study French or History is 40. 20 students study both. Subjects and the number of students who study French only is 10 more than the number who studied History only illustrate this information on a Venn diagram.
1) How many study French.
2) How much study History.
sorry - x take History only.
To solve this problem and illustrate the information on a Venn diagram, follow these steps:
1) Begin by drawing two overlapping circles representing French and History subjects.
2) Label the overlapping region as "French and History" since 20 students study both subjects.
3) Label the region outside both circles as "Neither French nor History," as it represents students who study neither subject.
4) Let "x" represent the number of students studying French only.
5) Since the number of students who study French only is 10 more than the number of students who study History only, label the region representing History only as "x - 10."
6) Label the region representing French only as "x."
7) According to the problem, the total number of students studying French or History is 40, so you can add up the number of students in all regions and equate it to 40:
x + (x - 10) + 20 + "Neither French nor History" = 40
Since the number of students in the "Neither French nor History" region is unknown, it is represented by "y" in this equation.
8) Simplify the equation:
2x - 10 + 20 + y = 40
2x + y = 30
9) To determine how many students study French (question 1), you need to find the value of "x."
To find how many students study History (question 2), you need to find the value of "x-10."
To find the values of "x" and "x-10," you need another equation or piece of information.
Help me to work it
Did you draw your Venn diagram? If so, then it should be clear that if x take French only, then
x+10 + 20 + x = 40