a small furniture factory makes three types of tables coffee tables dining tables and end tables. The factory needs to make 54 tables each day. The number of dining tables made per day should equal the number of coffee tables and end tables combine. The number of coffee tables maybe she should be three more than the number of end tables. write and solve a system equation to find the numbers of table of each type of factory should make each day.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

Variable x: Number of dining tables made.

Variable y: Number of coffee tables made.

Variable z: Number of end tables made.

The factory needs to make 54 tables each day, hence:

x + y + z = 54.

The number of dining tables made per day should equal the number of coffee tables, hence:

x = y.

Then, on the first equation:

2y + z = 54.

The number of coffee tables should be three more than the number of end tables, hence:

y = z + 3.

Replacing in the equation 2y + z = 54:

2(z + 3) + z = 54

3z = 48

z = 16.

Then:

y = z + 3 = 19.

x = y = 19.

The numbers of each machine made are given as follows:

Dining: 19

Coffee: 19

End: 16.

More can be learned about a system of equations at https://brainly.com/question/24342899

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