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?
If x passed history, then
x + x+9 - 75 = 156
Represent it on a Venn diagram
To find out how many students were taking each subject, we can use a method called Venn diagrams.
Let's represent the number of students taking geography as 'G' and the number of students taking history as 'H'.
From the given information, we know that 156 students passed geography or history. This means that the total number of students who passed can be represented as G + H - 75 (since we've counted the students who passed both subjects twice, so we subtract them once).
We also know that 9 more students passed geography than history. This can be written as G = H + 9.
Putting these two equations together, we have:
G + H - 75 = 156 - (i)
G = H + 9 - (ii)
Now we can solve these equations to find the values of G and H.
Substituting the value of G from equation (ii) into equation (i), we get:
(H + 9) + H - 75 = 156
2H - 66 = 156
2H = 222
H = 111
Substituting the value of H back into equation (ii), we get:
G = 111 + 9
G = 120
Therefore, there were 120 students taking geography and 111 students taking history.