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The staff at Tiny Little Cherubs day care center observed the eating habits of their 64 students during several
lunches. The saw that 59 children ate green beans, 56 ate cauliflower, 60 ate broccoli, 55 ate green beans and
cauliflower, 54 ate cauliflower and broccoli, 56 ate green beans and broccoli, and 53 ate all three.
How many children did not eat any of these vegetables? How many ate green beans but not cauliflower? How
many children did not eat broccoli? How many children ate only cauliflower? How many children ate exactly 2
types of vegetables?

Respuesta :

Hi there,

G = green beans

C = Cauliflower

B = broccoli

G + C = 55

C + B = 54

G + B = 56

G + B + C = 53

If 53 students ate all three, then 2 students ate just green beans and cauliflower (55-53)

If 53 students are all three, then 1 students ate just cauliflower and broccoli  (54-53)

If 53 students are all three, then 3 students ate just green beans and broccoli  (56-53)

So we have

53 eat G, B, C

2 eat G, C

1 eats C, B

3 eat G, B

---

59 students

Now, 59 students eat green beans, then 59-53-2-3= 1 eats green beans only

56 students eat cauliflower, then 56-53-2-1=0 no students eat just cauliflower

60 students eat broccoli, then 60-53-1-3 = 3 eat just broccoli

So now we have

53 eat G, B, C

2 eat G, C

1 eats C, B

3 eat G, B

1 eats G only

0 eat C only

3 eat B only

-----

63 students

But we have 64 students.  So one student doesn't eat any of the three vegetables.

3 students eat green beans but not cauliflower

3 students do not eat broccoli (2 +1)

0 students eat only cauliflower

4 students eat exactly two of the three vegetables.

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