In a school 156 passed Geography or history,75 students passed both subjects.If nine more passed Geography as passed history, how many students passed each subjects?

Answer 1

Let x be the number of students who passed only Geography, y be the number of students who passed only History, and z be the number of students who passed both subjects (75 students).

We know that:

x + y + z = 156 (Equation 1)

And we also know that:

x + z = (y + 9) (Equation 2)

This is because nine more students passed Geography than History, which means that the number of students who passed both subjects is equal to the number of students who passed History plus nine.

We can use equation 2 to solve for x in terms of y and z:

x = y + 9 - z

We substitute this expression for x into equation 1:

(y + 9 - z) + y + z = 156

Simplifying:

2y + 9 = 156

2y = 147

y = 73.5

This doesn't make sense since y must be a whole number. However, we do know that y + z = 75, which means that z = (75 - y). We can substitute this expression for z into equation 2:

x + (75 - y) = (y + 9)

Simplifying:

x = y + 9 - 75 + y

x = 2y - 66

Now we can substitute this expression for x into equation 1:

(2y - 66) + y + 75 = 156

Simplifying:

3y = 147

y = 49

Now that we know y, we can use y + z = 75 to solve for z:

49 + z = 75

z = 26

Finally, we can use x = 2y - 66 to solve for x:

x = 2(49) - 66

x = 32

Therefore, 32 students passed only Geography, 49 students passed only History, and 26 students passed both subjects.