Question

A dining hall had a lotal of 15 tables - some long rectangular tables and some round ones. Long tables can

eat 12 people and round tables can seat 8 people. On a busy evening, all 156 seats are occupied. How many long tables, x, and round tables, y, are used if all seats are occupied?

Answer 1

there are 15 long tables and 0 round tables

Explanation:

You can set up two equations to represent the number of people seated at each type of table. Let x be the number of long tables and y be the number of round tables. The first equation is: 12x + 8y = 156. This equation represents the total number of people seated, with 12 people seated at each long table and 8 people seated at each round table.

The second equation represents the total number of tables: x + y = 15.

You can solve this system of equations using substitution. First, solve for x in the second equation by subtracting y from both sides: x = 15 - y. Substitute this expression for x into the first equation: 12(15 - y) + 8y = 156.

This simplifies to: 180 - 12y + 8y = 156.

Combining like terms, we get: -4y = 24.

Dividing both sides by -4, we get: y = -6.

Since y represents the number of tables, and we can't have negative tables, this solution is not valid. Therefore, there are no round tables.

Substituting y = 0 into the equation x + y = 15, we get: x + 0 = 15. Solving for x, we find that there are 15 long tables.

Therefore, there are 15 long tables and 0 round tables.