To solve this problem, we need to use the given information and break it down step by step.
Let's start by understanding the pattern in the number of chairs for every second row. We are told that the difference between the number of chairs in each pair of consecutive rows is constant. In other words, the number of chairs increases by the same amount for each pair of rows.
Let's denote the number of chairs in the first two rows as "x". According to the given information, x = 27.
Next, we know that the number of chairs in the third and fourth rows is three more than the first two rows. This implies that the number of chairs in the third and fourth rows is x + 3.
Similarly, the number of chairs in the fifth and sixth rows will be three more than the third and fourth rows. Therefore, the number of chairs in the fifth and sixth rows is (x + 3) + 3, which simplifies to x + 6.
We can continue this pattern: for every second pair of rows, the number of chairs will be three more than the previous pair. So for the seventh and eighth rows, the number of chairs will be (x + 6) + 3, which simplifies to x + 9.
We are also given that the last two rows each have 114 chairs. Denoting the number of chairs in the last two rows as "y," we have y = 114.
Now, let's find the value of x. We know that x = 27, so substituting this value into the equation, we have 27 + 9 = 36. Therefore, the number of chairs in the seventh and eighth rows is 36.
Continuing this pattern, we can see that for every second pair of rows, the number of chairs increases by 3. So, the number of chairs in the ninth and tenth rows would be 36 + 3 = 39.
Now let's find the number of chairs in the last two rows, y = 114. Substituting the values we know, y = 39 + 3 = 42.
From the information given, we have that the last two rows each have 114 chairs. Therefore, the number of rows in total can be found by dividing 114 by the number of chairs in the last two rows: 114 / 42 = 2.7.
However, we cannot have a fraction of a row since rows are whole units. Therefore, we need to consider the ceiling or rounding up when converting to a whole number.
Therefore, the answer is that there are a total of 3 rows of chairs in the auditorium.
I hope this explanation helps clarify the solution to the problem. Let me know if you have any further questions!