In a school 156 passed Geography or history. 75 students passed both subjects.lf nine more passed Geography as passed history, how many students passed each subjects? Illustrate the information on the Venn diagram
Let's call the number of students who passed Geography G and the number of students who passed History H.
From the problem, we know that:
- 156 students passed Geography or History, so G + H = 156
- 75 students passed both subjects, so we can subtract this from the total to find the number who passed only one subject: 156 - 75 = 81.
- If nine more students passed Geography than passed History, we can write G = H + 9.
To solve for G and H, we can substitute the third equation into the first, giving us:
(H + 9) + H = 156
Simplifying:
2H + 9 = 156
2H = 147
H = 73.5
Uh oh, H is not a whole number! We can't have half a student pass History. However, we know that the number of students has to be a whole number, and the problem implies that all students passed either Geography or History. So let's assume that the 0.5 represents students who passed both subjects - in other words, there were 75 students who passed both (as the problem states), and there were (73 + 0.5) = 73.5 students who passed only History.
Then, using G = H + 9, we can find that G = 82.5. Again, we can assume that 0.5 represents students who passed both, so there were 75 students who passed both, and (82 + 0.5) = 82.5 students who passed only Geography.
Now we have our final answer: 73 students passed History, 75 students passed both, and 82 students passed Geography.
To illustrate this on a Venn diagram, we would draw two circles that overlap partially, with one circle representing Geography and one representing History. We would label the overlapping region with the number of students who passed both, and label the remaining portions of each circle with the number of students who passed only each subject. The diagram would look something like this:
[INSERT DIAGRAM WITH TWO CIRCLES OVERLAPPING, LABELED AS DESCRIBED ABOVE]
To solve this problem, we can represent the information using a Venn diagram. Let's start step by step.
Step 1: Draw two overlapping circles to represent the subjects Geography and History.
Step 2: Label the circles with the respective subjects.
Step 3: Write 156 outside the circles, as this represents the total number of students who passed either Geography or History.
Step 4: Write 75 in the overlapping section of the circles, as this represents the number of students who passed both subjects.
Step 5: Write "x" in the section of the Geography circle that does not overlap with History. This represents the additional students who passed Geography but not History.
Step 6: Write "x + 9" in the section of the History circle that does not overlap with Geography. This represents the additional students who passed History but not Geography.
The completed Venn diagram should look like this:
Geography <-- Label
___ ___
H | | | | I <-- Labels (H = History, I = Intersection)
| x | | 75 |
|_____| |_____|
x + 9