Answer:
182 sandwiches
Step-by-step explanation:
How many sandwiches only included sprouts (of these three ingredients)
Total sandwiches = 295
68sandwiches included turkey
53 sandwiches included cheese
15 sandwiches included both turkey and cheese
9 sandwiches included turkey and sprouts
7 sandwiches included both cheese and sprouts
5 sandwiches included all three ingredients
18 sandwiches had none of these ingredients (turkey, cheese, or sprouts)
Let's represent
Turkey = T
Sprouts = S
Cheese = C
n (T ∪ S ∪ C) - n(none of the ingredients) = n(T ) + n ( S ) + n (C) - n ( T ∩ S) - n ( T ∩ C) - n ( C ∩ S) + n (T ∩ S ∩ C )
= 295 - 18 = 68 + 53+ n(S) - 9 - 15 - 7+ 5
= 277 = 121 + n(S) - 26
= 277 - 121 + 26= n(S)
= 303 - 121 = n(S)
= 182 = n(s)
Hence, only 182 sandwiches had only sprouts
