A restaurant has tables that can seat either 4 or 7 persons. there are 12 four seaters and 8 seven seater tables.
a) what is the largest number of persons that can be seated if all the four seater tables only are occupied?
b) 83 persons are to be seated for lunch. All the four seaters must be used. What is the least number of six seaters that would be used?
c) On Wednesday 63 persons are to be seated. How many of each type of tables are needed so that all seats are occupied and both types of tables are used?
d) If all seats have been used up, what fraction of the people present used up the seven seaters tables?
can u please answer my question
Yes, I can answer your question, but I want to see your work first. For instance, I'm sure you can answer the first question.
48
48
a) To find the largest number of persons that can be seated if all the four-seater tables only are occupied, we need to multiply the number of four-seater tables by the seating capacity of each table.
There are 12 four-seater tables, and each table can seat 4 persons. Therefore, the total number of seats available in the four-seater tables is 12 * 4 = 48.
So, the largest number of persons that can be seated if all the four-seater tables only are occupied is 48.
b) If all the four-seater tables must be used to seat 83 persons, we first use up all the four-seater tables. There are 12 four-seater tables, and each table can seat 4 persons. So, the total capacity of the four-seater tables is 12 * 4 = 48.
To find the number of six-seater tables needed, we subtract the capacity of the four-seater tables from the total number of persons to be seated: 83 - 48 = 35.
Since each six-seater table can seat 6 persons, we divide the remaining number of persons by 6 to see how many six-seater tables are needed: 35 / 6 = 5 with a remainder of 5.
Therefore, the least number of six-seater tables that would be used is 5.
c) To seat 63 persons while using both types of tables, we first use up the four-seater tables. There are 12 four-seater tables, and each table can seat 4 persons. So, the total capacity of the four-seater tables is 12 * 4 = 48.
To seat the remaining persons with the seven-seater tables, we subtract the capacity of the four-seater tables from the total number of persons to be seated: 63 - 48 = 15.
Since each seven-seater table can seat 7 persons, we divide the remaining number of persons by 7 to see how many seven-seater tables are needed: 15 / 7 = 2 with a remainder of 1.
Therefore, we would need 2 seven-seater tables and 1 four-seater table to seat all 63 persons.
d) If all seats have been used up, we have a total capacity of 12 * 4 + 8 * 7 = 48 + 56 = 104.
To find the fraction of people who used the seven-seater tables, we need to divide the capacity of the seven-seater tables by the total capacity.
Capacity of the seven-seater tables = 8 * 7 = 56
Total capacity = 104
Fraction of people who used the seven-seater tables = Capacity of the seven-seater tables / Total capacity = 56 / 104 = 7 / 13.
Therefore, the fraction of people present who used up the seven-seater tables is 7/13.