Question

A restaurant offers a buffet dinner at prices.it costs $10 for one person $20 for two $29 for three $37 for four $44 for five and so on

a.) How much does a buffet dinner for 8 cost ? how much does a group of eight save if its members eat together rather than alone?

b.) the buffet cost the restaurant $6 per person. how large a group can the restaurant serve without losing money?

Answer 1

a.) find the pattern....
difference between 10 and 20 = 10
difference between 20 and 29 = 9
difference between 29 and 37 = 8
difference between 37 and 44 = 7
Do you see the pattern.....you will add 6 to the next number and add 5 to the number after that...etc
44 + 6 = 50 (for 6)
50 + 5 = 55 (for 7)
55 + 4 = 59 (for 8)
So a buffet dinner for 8 costs $ 59.
If they eat alone it would cost $ 80...so by eating together they save (80 - 59) = $ 21

b.) The buffet cost the restaurant $ 6 per person.
We already know it costs $ 59 for 8 and $6 per person for 8 costs $ 48...the restaurant can get more people without losing money...lets try a group of 9...If it's $ 59 for 8 and we added 4 to get that, then for 9 people we will have to add 3....59 + 3 = 62(it's 62 for 9) and 6 * 9 = 54...add more people....62 + 2 = 64 (for 10).lets try more people because 6 * 10 = 60...64 + 1 = 65 (for 11) and 6 * 11 = 66 .....oops, if the restaurant served a group of 11 for $ 65 and they paid $ 66 . they would lose money...so, without losing money, they could serve a group of 10 for $ 64 and it would cost the restaurant $ 60.