Question

a dining hall had a total of 25 tables—some long rectangular tables and some round ones. long tables can seat 8 people. round tables can seat 6 people. on a busy evening, all 190 seats at the tables are occupied.
write a system of equations that represent the situation, the first equation is the total number of tables and the second equation is the total amount of people seated at the tables
let x = ____
let y = ____
equation 1: ____
equation 2: ____
how many long tables, and how many round tables are there?

Explanation:

Step1: Define variables

Let \( x \) = number of long tables, \( y \) = number of round tables.

Step2: Write Equation 1 (total tables)

The total number of tables is 25, so \( x + y = 25 \).

Step3: Write Equation 2 (total people)

Long tables seat 8, round seat 6, total 190. So \( 8x + 6y = 190 \).

Step4: Solve the system

From Equation 1: \( y = 25 - x \). Substitute into Equation 2:
\( 8x + 6(25 - x) = 190 \)
\( 8x + 150 - 6x = 190 \)
\( 2x = 40 \)
\( x = 20 \).

Step5: Find \( y \)

Substitute \( x = 20 \) into \( y = 25 - x \):
\( y = 25 - 20 = 5 \).

Answer:

Long tables: 20, Round tables: 5