I'm really struggling with this --
I have different table configurations - straight line, L-shaped, plus sign-shaped, and T-shaped. Suppose there are n tables arranged in these patterns. I need to write an expression of the number of tables with 2 chairs. Our teacher gave us the first answer for the straight line - n - 2 and we have to come up with the other three but I do not understand where the n - 2 came from so I don't know how to do the others.
Please help!!
Is there a picture that would help explain your predicament better? Also, what type of math is this (geometry,algebra,calculus, if you don't know you can reply with the grade number math your doing. 5th grade math,4th grade math, etc.)
It's called math literacy. There are pictures but they don't help. They are just squares in a straight line, in a l shape, a t shape, and a plus sign
I apologize Carly for not answering better. I have NO idea what math literacy is. I apologize. I know geometry, algebra, and anything else lower than that. I apologize for the delay, you may want to ask your teach what the answer is though.
Sure! I can help you understand where the expression "n - 2" comes from for the straight line configuration.
Let's start by considering a straight line of tables. Each table in the line, except for the first and last one, will have two neighboring tables. This means that each table, except for the first and last one, will have two chairs.
Now, let's think about the chairs. The first table in the line will have a chair only on its right side, and the last table will have a chair only on its left side. So, these two tables will each have only one chair. The remaining tables in the line, except for the first and last ones, will have chairs on both sides, resulting in two chairs per table.
To calculate the number of tables with two chairs in a straight line configuration, we need to subtract the number of tables that have only one chair (the first and last tables) from the total number of tables, which is represented by "n."
Therefore, the expression for the number of tables with two chairs for the straight line configuration is given by "n - 2." The "n" represents the total number of tables, and subtracting 2 accounts for the first and last tables with only one chair each.
To find the expressions for the L-shaped, plus sign-shaped, and T-shaped configurations, let's analyze each one:
1. L-shaped configuration:
In an L-shaped configuration, two tables meet at a right angle, forming an "L" shape. There are several ways the tables can be arranged in this shape, such as having two tables placed horizontally and one vertically or vice versa.
To determine the expression for the number of tables with two chairs, we need to consider the tables at the corner of the "L." Since there are two tables in the corner, both of them will have only one chair. Therefore, the expression for the L-shaped configuration can be represented as "n - 2."
2. Plus sign-shaped configuration:
In a plus sign-shaped configuration, one table is placed in the center, and four tables surround it, forming a plus sign. To find the expression, we need to identify tables with only one chair.
In the plus sign shape, the center table will have four neighboring tables, so it will have four chairs. However, the tables on the arms of the plus sign will have only one neighboring table, so they will have two chairs.
To determine the expression for the number of tables with two chairs, we subtract the center table with four chairs from the total number of tables, which is represented by "n." Therefore, the expression for the plus sign-shaped configuration is "n - 1 - 4," where "n - 1" represents all the tables except the center table and the "- 4" accounts for the four chairs on the center table.
3. T-shaped configuration:
In a T-shaped configuration, one table is placed at the top, and three tables surround it, forming a "T" shape. To find the expression, we need to identify tables with only one chair.
Similarly to the plus sign-shaped configuration, the center table will have three neighboring tables, so it will have three chairs. The tables on the arms of the "T" will have only one neighboring table, so they will have two chairs.
To determine the expression for the number of tables with two chairs, we subtract the center table with three chairs from the total number of tables, which is represented by "n." Therefore, the expression for the T-shaped configuration is "n - 1 - 3," where "n - 1" represents all the tables except the center table, and the "- 3" accounts for the three chairs on the center table.
I hope this explanation helps you understand how to find the expressions for the different table configurations! Let me know if you have any further questions.