Guide 1/Algebra, Page 146, Question #10

[choeestelle]

Question: At a graduation, guests sit in rows such that there are p people in the first row, p+1 people sit in the second row, p+2 people sit in the third row, and so on. How many more people sit in row n than in the second row?

I don't understand how the answer to this question is n-2.

Thanks for your help.

[tommywallach]

Question: At a graduation, guests sit in rows such that there are p people in the first row, p+1 people sit in the second row, p+2 people sit in the third row, and so on. How many more people sit in row n than in the second row?

I don't understand how the answer to this question is n-2.

Hey Choee,

On a question like this, the best thing is just to work it out with some examples. Imagine that p = 1. Then, each row will simply have the same number of people as its row number. Now, let's create a few sample row n's:

n = 10 --> how many more than row 2? --> 8
n = 15 --> how many more than row 2? --> 13
n = 20 --> how many more than row 2? --> 18

Notice that, in each case, row n has (n-2) more seats than the second row. Even though we set p = 1, the same would be true no matter what p is, because each row still just goes up by 1. The starting point is irrelevant.

Hope that helps!

-t