Answer:
(a) 4 y + 6 s = 116 represents the given situation.
(b)There are 8 six- person tables at the party.
Step-by-step explanation:
Here, the total number of tables = 25
Let y : Represent the number of four person tables.
s : Represents the number of six person tables.
Total people seated at all tables = 116
Now, the number of people seated at table of 4 = y x 4 = 4 y
the number of people seated at table of 6 = s x 6 = 6 s
(a) Total People Seated = People seated at { 4- table + 6 table}
⇒ 116 = 4 y + 6 s
Hence, 4 y + 6 s = 116 represents the given situation.
(b) Total tables are 25. ⇒ s + y = 25
Hence, the givens system of equations are:
4 y + 6 s = 116 ........ (1)
s + y = 25 ............ (2)
Solving the above system, we get, substitute y = 25 - s in (1)
4 y + 6 s = 116 ⇒ 4(25-s) + 6s = 116
or, 100 - 4s + 6s = 116
or. 2s = 16
or, s = 16 / 2 = 8 ⇒ s = 8
Hence, there are 8 six- person tables at the party.
