In a school, 156 students passed geography or history. There were 75 students who passed in both subjects. If 9 more passed Geography than history, find how many were taking each subject

not enough information to find "how many were taking each subject"

... can find how many passed each subject
... but no information on how many failed ... taking = passed + failed

75 passed both ... so (156 - 75) passed one or the other
... 9 more G than H ... G or H is 81 students

G = H + 9 ... 2 H + 9 = 81 ... solve for H , substitute back to find G

remember to add in the 75 who passed both

Eric

Well, in terms of subject popularity, I guess that means more students are "getting their bearings" in Geography... or maybe they just prefer to avoid a "history of bad grades." Either way, let's try to figure this out!

Let's assume that the number of students taking history is "x." Since 9 more students passed Geography than history, then the number of students taking Geography is "x + 9".

Now, we know that there were 156 students in total who passed either geography or history. Since 75 students passed both subjects, we can set up an equation to represent this information:

x + (x + 9) - 75 = 156

Combining like terms, we have:

2x + 9 - 75 = 156

Doing some math...

2x - 66 = 156

And now, for the moment of truth:

2x = 222

Dividing both sides by 2, we find:

x = 111

So, there were 111 students taking history, and since 9 more passed Geography, the number of students taking that subject is 111 + 9 = 120.

There you have it! 111 brave students delving into history, while 120 adventurous souls explore the world of Geography.

Let's assume the number of students taking history as x.

According to the given information:
- Number of students passed in history = x
- Number of students passed in geography = x + 9
- Number of students passed in both subjects = 75

Now, to find the total number of students who passed in geography or history, we add the number of students passing in each subject:
Total = Number passed in history + Number passed in geography - Number passed in both
156 = x + (x + 9) - 75

Simplifying the equation:
156 = 2x + 9 - 75
156 + 75 - 9 = 2x
222 = 2x
x = 111

So, the number of students taking history is 111, and the number of students taking geography is 111 + 9 = 120.

To solve this problem, we can use a method called the Venn diagram.

Step 1: Draw two intersecting circles, one for geography and one for history.
Step 2: Let x represent the number of students who passed in history. Since 9 more students passed in geography, the number of students who passed in geography will be x + 9.
Step 3: Write down the total number of students who passed in both subjects, which is 75, in the intersection of the two circles.
Step 4: Write down the total number of students who passed in geography only as x + 9 - 75, and write down the total number of students who passed in history only as x - 75.
Step 5: Write down the total number of students who passed in geography or history, which is 156, as the summation of the four regions in the Venn diagram: (x - 75) + (x + 9 - 75) + 75 + x = 156.
Step 6: Simplify the equation: 3x - 216 = 156.
Step 7: Solve for x: 3x = 372.
Step 8: Divide both sides by 3: x = 124.

Hence, 124 students were taking History and 124 + 9 = 133 students were taking Geography.