Please help. 1. Participants at a two-day conference could register for only one

Question

Please help.

1. Participants at a two-day conference could register for only one of the days (Friday or Saturday) or for both days (Friday and Saturday). There were 231 participants on Friday and 252 participants on Saturday. The total number of people who registered for the conference was 350. How many participated in the conference on both days?

2. A diner serves a bargain breakfast which includes eggs (over-easy, poached, or scrambled); pancakes or toast; and juice (orange, tomato, or grapefruit). A breakfast must include one selection from each category. What are the different possible breakfasts? How many possible breakfasts are there?

3.A local Pizza Hut manager decided to offer a pizza special. The special was limited to cheese pizzas with or without sausage and with a choice of thin crust, thick crust, or stuffed crust. How many different versions of pizza are possible?

Explanation / Answer

Solution

Q1

Let x = number of participants who participated on both days.

Now,

Total number of participants who registered for the conference = number of participants who could register for Friday only + number of participants who could register for Saturday only + number of participants who registered for both Friday and Saturday………………………...........................................................................................(1)

Now,

Number of participants who could register for Friday = number of participants who could register for Friday only + number of participants who registered for both Friday and Saturday or

Number of participants who could register for Friday of participants who could register for Friday - number of participants who registered for both Friday and Saturday

= 231 – x ………………………………………………………………………………………(2)

Number of participants who could register for Saturday = number of participants who could register for Saturday only + number of participants who registered for both Friday and Saturday or

Number of participants who could register for Saturday of participants who could register for Saturday - number of participants who registered for both Friday and Saturday

= 252 – x ………………………………………………………………………………………(3)

(1), (2) and (3) => 350 = (231 – x) + (252 – x) + x or x = 231 + 252 – 350 = 133 ANSWER

Q2

The breakfast must have one selection out of 3 options available on eggs, either pancake or toast (i.e. 2 options) and one selection out of 3 options available on juice. Thus, total number of combinations is: 3 x 2 x 3 = 18 ANSWER

Q3

The pizza must have one selection out of 2 options available on sausages and one selection out of 3 options available on crust. Thus, total number of combinations is: 2 x 3 = 6 ANSWER

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