A banquet hall is divided into two sections that both have tables with chairs arranged around them. In the smaller section, there are 9 tables with 6 chairs each. In the larger section, there are currently 4 tables with 8 chairs each. More tables, each with 8 chairs, will be added to this larger section so that there will be 126 total chairs in the banquet hall. Which equation could be used to determine how many more tables, t, each with 8 chairs, are needed in the larger section?

The equation that could be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section is

8t + 86 = 126 OR 8t = 40

Step-by-step explanation:

From the question,

In the smaller section of the banquet hall, there are 9 tables with 6 chairs each.

This means there are 9 × 6 chairs there

9 × 6 = 54

Hence, there are 54 chairs in the smaller section of the banquet hall.

Also, from the question,

In the larger section of the banquet hall, there are currently 4 tables with 8 chairs each.

This means there are 4 × 8 chairs there presently

4 × 8 = 32

Hence, there are currently 32 chairs in the larger section of banquet hall.

From the question,

More tables, each with 8 chairs, will be added to this larger section so that there will be 126 total chairs in the banquet hall.

If t more tables are to be added,

This means that t × 8 (8t) chairs will be added to the larger section so that there will be 126 total chairs in the banquet hall.

The total chair in the banquet hall will be = Total number of chairs in the smaller section + Current number of chairs in the larger section + Number of chairs to be added to the larger section

Therefore,

126 = 54 + 32 + 8t

126 = 86 + 8t

Then,

8t + 86 = 126

8t = 126 - 86

8t = 40

This equation can be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section.

Hence, the equation that could be used to determine how many more tables, t, each with 8 chairs, that are needed in the larger section is

8t + 86 = 126 OR 8t = 40.

If desired,

8t = 40

t = 40/8

t = 5

Hence, 5 more tables are needed in the larger section.