Question

The staff at Tiny Little Cherubs day care center observed the eating habits of their 64 students during several

Answer 1

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

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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

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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.