Question

In a restaurant there are 16 tables, each having either 3, 4 or 6 chairs. Together, the tables having 3 or 4 chairs can accommodate 36 people. Knowing that the restaurant can accommodate 72 people, how many tables are there with 3 chairs? ​

Answer 1

Answer:

If the tables with 3 or 4 chairs can accommodate 36 people, then the tables with 6 chairs can accommodate (72–36=) 36 people.

So there are (36/6=) 6 tables with 6 chairs.

that leaves us with (16–6=) 10 tables with either 3 or 4 chairs. Let the number of tables with 3 chairs be x and the number of tables with 4 chairs be y.

we therefore know that

3x + 4y = 36 (we can seat 36 people at the tables)

and

x + y = 10 (there are 10 tables)

rearranging the second equation, we get x = 10-y

substituting that into the first equation we get

3(10-y) + 4y = 36

30 - 3y + 4y = 36

30 + y = 36

y = 6

x + y = 10

so x = 10 - y (6)

x = 4

check:

3*4 + 4*6 = 36 (12+24=36)

so there are 4 tables with 3 chairs, 6 tables with 4 chairs and 6 tables with 6 chairs.

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