Question 1019852
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.