How many customers didn't put any toppings, and how many had ketchup?
A hamburger seller offers its customers Ketchup, Mustard, and Relish as toppings. The following table shows the toppings selected by the 1600 customers who bought hamburgers from them. (All inclusive)
Topping / Number Of Customers
Ketchup & Mustard 551
Ketchup & Relish 318
Mustard & Relish 186
All Three 186
a) How many customers didn't put any toppings?
b) How many put ketchup?
We can do this using set theory and set calculations. I will use the following notations.
Ketchup - K
Mustard - M
Relsih - R
Therefore according to given data.
`S = 1600`
`K = 944`
`M = 771`
`R = 656`
`K nn M = 551`
`K nn R = 318`
`M nn R = 186`
`K nn M nn R = 186`
Let's find first how many customers did put toppings.
`K uu M uu R`
According to set rules,
`K uu M uu R = K + M + R -(K nn M) - (K nn R) - (M nn R) + (K nn M nn R)`
`K uu M uu R =944+771+656-551-318-186+186`
`K uu M uu R = 1502`
Therefore, the number of customers who had one or more toppings is 1502.
Therefore number customers who didn't get toppings
The number of customers who put only ketchup = K1
`K1 = K -(K nn M) - (K nn R) + (K nn M nn R)`
`K1 = 944 -551-318+186`
`K1 = 261`
Therefore, the number of customers who got only ketchup is 261.