In a group of 50 patrons, 8 patrons like lattes and espressos, 12 patrons like espressos and cappuccinos, 9 patrons like lattes and cappuccinos, and 5 patrons like all 3 coffee drinks. Altogether, 20 patrons like lattes, 28 patrons like espressos, and 19 patrons like cappuccinos. How many patrons don't like any of these coffee drinks?.

A. 9.
B. 4.
C. 3.
D. 7

Respuesta :

frika

Let's count how many patrons like only two of these coffe drinks:

1. If 5 patrons like all 3 coffee drinks and 8 patrons like lattes and espressos, then 8-5=3 like only lattes and espressos.

2. If 5 patrons like all 3 coffee drinks and 12 patrons like espressos and cappuccinos, then 12-5=7 like only espressos and cappuccinos.

3. If 5 patrons like all 3 coffee drinks and 9 patrons like lattes and cappuccinos, then 9-5=4 like only lattes and cappuccinos.

Let's count how many patrons like only one of these coffe drinks:

1. For espresso:

a) 5 patrons like all 3 coffee drinks

b) 3 patrons like only lattes and espressos

c) 7 patrons like only espressos and cappuccinos

d) 28 patrons like espressos

Then 28-5-3-7=13 patrons like espressos.

2. For cappuccino:

a) 5 patrons like all 3 coffee drinks

b) 4 patrons like only lattes and cappuccinos

c) 7 patrons like only espressos and cappuccinos

d) 19 patrons like cappuccinos

Then 19-5-4-7=3 patrons like cappuccinos.

3. For lattes:

a) 5 patrons like all 3 coffee drinks

b) 4 patrons like only lattes and cappuccinos

c) 3 patrons like only lattes and espressos

d) 20 patrons like lattes

Then 20-5-4-3=8 patrons like lattes.

Add all numbers that denote one, two or all three drinks patrons:

8+3+13+3+7+4+5=43 patrons that like some of coffee drinks. In total there are 50 patrons, then 50-43=7 patrons don't like any of these coffee drinks.

Answer: 7 patrons, correct choice is D.