A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are
I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric Train
How many students are in the event Watches Little Galileo and Super Reader?
A)
23
B)
32
C)
167
D)
240
4 answers
Ms sue. Can you help. I don’t know where to start to figure this out. Maybe a Venn diagram
Yes, a Venn diagram,
3 intersecting circles G, S, and T within a rectangle
We are not given the intersection of all 3 circles, so put in x in that intersection
- 22 preschoolers did not watch any of these shows, ... so put 22 outside the circles but inside the rectangle.
- 22 preschoolers did not watch any of these shows, .... so put 73 in the G circle part not intersecting with any of the others.
- 31 preschoolers only watched Little Galileo and Prehistoric Train, .... so you already have the intersection of all three marked as x, so the missing part of G and P is 31-x, put it in
- 136 preschoolers watched Little Galileo, ... label the intersection of G and S, but not P as y
y + x + 31-x + 73 = 136
y = 32 , put that in for y
- 14 preschoolers only watched Super Reader and Prehistoric Train, .... just as before put in
14-x for S and P, but not G
- 63 preschoolers watch Super Reader, let only S be k
k + x + 14-x + 32 = 63
k = 17 , put that in
continue in this way ....
3 intersecting circles G, S, and T within a rectangle
We are not given the intersection of all 3 circles, so put in x in that intersection
- 22 preschoolers did not watch any of these shows, ... so put 22 outside the circles but inside the rectangle.
- 22 preschoolers did not watch any of these shows, .... so put 73 in the G circle part not intersecting with any of the others.
- 31 preschoolers only watched Little Galileo and Prehistoric Train, .... so you already have the intersection of all three marked as x, so the missing part of G and P is 31-x, put it in
- 136 preschoolers watched Little Galileo, ... label the intersection of G and S, but not P as y
y + x + 31-x + 73 = 136
y = 32 , put that in for y
- 14 preschoolers only watched Super Reader and Prehistoric Train, .... just as before put in
14-x for S and P, but not G
- 63 preschoolers watch Super Reader, let only S be k
k + x + 14-x + 32 = 63
k = 17 , put that in
continue in this way ....
Yay!!!!! Thanks so much.
Thanks for getting me started Reiny
1 answer