SOLUTION: A restaurant has only two person tables and four person tables. There are 16 tables in all that can seat a maximum of 50 people. How many two person and how many four person tables

Question 1019852: A restaurant has only two person tables and four person tables. There are 16 tables in all that can seat a maximum of 50 people. How many two person and how many four person tables are there?
Found 3 solutions by LinnW, Cromlix, addingup:
Answer by LinnW(1048)   (Show Source): You can put this solution on YOUR website!
Let T be the number of two person tables.
Let F be the number of four person tables.
T + F = 16
two times the number of two person tables + 4 times the number of 4 person tables is 50
2T + 4F = 50
Working with T + F = 16 , add -T to each side
F = 16 - T
Substitute (16 - T) for F in 2T + 4F = 50
2T + 4(16 - T) = 50
2T + 64 -4T = 50
-2T + 64 = 50
add -64 to each side
-2T = -14
Divide each side by -2
T = 7
Since F = 16 - T , F = 16 - 7 , F = 9
Let's check our original equations.
T + F = 16 , 7 + 9 = 16 so this checks out
2T + 4F = 50 , 2(7) + 4(9) = 50 , 14 + 36 = 50 so this one works.
We have 7 two person tables, and 9 four person tables.
Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
Hi there,
make 2 person tables = 'x'
and 4 person tables = 'y'
x + y = 16.......(1)
2x + 4y = 50.....(2)
Multiply (1) by 2
2x + 2y = 32.....(1)
2x + 4y = 50.....(2)
Subtract (1) from (2)
.....2y = 18
......y = 9
Substitute y = 9 into (10
x + y = 16.......(10
x + 9 = 16
x = 16 - 9
x = 7
7 two person tables
9 four person tables.
Hope this helps :-)
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
Two person: x
Four person: y
x+y = 16 and so: x = 16-y We'll use this value for x next.
2x+4y = 50 substitute for x:
2(16-y)+4y = 50
32-2y+4y = 50
2y = 18
y = 9 There are 9 four-person tables and
16-9 = 7 two-person tables
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check (always check):
9*4 = 36
7*2 = 14
______-----
Total: 50 We have the correct answer
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