Question

A party is thrown where 25 tables are used. Each table either sits 4 people or 6 people. A total of 116 people can be sat at the tables.

a) If y represent the number of four person tables and s represents the number of six person tables, write a
system of equations that models this situation.

b) How many six person tables are there?​

Answer 1

(a) 4 y + 6 s = 116 represents the given situation.

(b)There are 8 six- person tables at the party.

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.