Asked by MUHAMMAD
80 boys took the GCE examination in the three subjects geography, English and mathematics and none of them failed all three subjects, it was noted that 8 passed English only and 10 passed mathematics only, 7 passed mathematics and geography but not English, 40 passed English and mathematics and 21 passed English and geography, altogether 54 passed English.
(a) Draw a venn diagram to represent this information
(b)from venn diagram, find the number of pupils who
(i) Passed geography only,
(ii) Passed all three subjects
(a) Draw a venn diagram to represent this information
(b)from venn diagram, find the number of pupils who
(i) Passed geography only,
(ii) Passed all three subjects
Answers
Answered by
oobleck
If you draw the diagram, you can see that since 54 passed English, and 17 passed only Math and Geography, only 9 passed Geography only.
So, if we let
x = english and math only
y = english and geography only
z = all three, then we have
x+z = 40
8+y+z = 21
8+x+y+z = 54
Solve those to find x,y,z and then
(i) already noted to be 9
(ii) 7
So, if we let
x = english and math only
y = english and geography only
z = all three, then we have
x+z = 40
8+y+z = 21
8+x+y+z = 54
Solve those to find x,y,z and then
(i) already noted to be 9
(ii) 7
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