Question 1004859: There are 16 tables at a certain restaurant. The tables can seat either 3, 4 or 6 people. Altogether, the restaurant has 72 seats. The tables with 3 or 4 seats can seat 36 people altogether. How many tables with 3 seats exist at this restaurant?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! There are 16 tables at a certain restaurant.
The tables can seat either 3, 4 or 6 people.
Altogether, the restaurant has 72 seats.
The tables with 3 or 4 seats can seat 36 people altogether.
How many tables with 3 seats exist at this restaurant?
:
Let the letters, a, b, c = the 3, 4, 6 seat tables respectively
:
Tables:
a + b + c = 16
Seats:
3a + 4b + 6c = 72
"The tables with 3 or 4 seats can seat 36 people altogether.":
3a + 4b = 36
:
Use elimination with the last two equation
3a + 4b + 6c = 72
3a + 4b + 0c = 36
-------------------Subtraction eliminates a and b find c
6c = 36
c = 36/6
c = 6 tables
therefore
a + b = 16 - 6
a + b = 10 tables
b = (10 - a)
Back to the 3rd equation, 3a + 4b = 36, replace b with (10-a)
3a + 4(10-a) = 36
3a + 40 - 4a = 36
3a - 4a = 36 - 40
-a = -4
a = 4 tables the seat 3
|
|
|
