Algebra Book (Guide # 1), Question # 10, Page 154 (4th Ed)

[divinedookie]

I carefully read and reviewed question 10 on page 154 (and the answer on page 158. I do not understand how the formula p + (n-1) is established.

[tommywallach]

Just think about it logically. Every row has one more than the row before it, so you could conceivably just think

If row n = 5, then the second row had 2 people, so the difference is 3 (which is n-2)

If row n = 6, then the second row still had 2 people, so the difference is 4 (which is n-2).

Hope that helps!

-t

[divinedookie]

Great, thank you. The way you explained it makes so much more sense than the way detailed in the answer.

[tommywallach]

Glad to help!

-t

[dpbowen]

Hey! Sorry to be late to the party, but I'm having issues with question 10 on page 154 as well.

n-2 would be the difference between rows n and 2 if there was one person in the first row, but we don't know that because it doesn't say that there is one person in the first row; there are "p" people in the first row.

There could be three people in the first row, and the second row would be
p + 1/ (3) + 1= 4.

if the nth row has 7 people, the difference would be 3; 7 - 3 + 1 = 3. Or, n - 4

I'm still not understanding how the answer is being derived.

[tommywallach]

Hey Dp,

Your logic is off. It doesn't matter how many the first row has if they keep going up by one each time. Addition doesn't change based on where you start. It's a number line.

BUT, to illustrate your error:

If there are 3 people in the first row (so = 3), the second row has 4 people, and so on.

The mistake you made here is just DETERMINING the number of people in the nth row. That's not legal. You can plug in a value FOR n, then USE that to determine the number of people. (You can't just assign it randomly, because you already set a value for the first row, so the nth row is DEFINED).

If n =7, as you (sorta) suggested, then we would count up.

Row 1 = 3 people
Row 2 = 4
Row 3 = 5
Row 4 = 6
Row 5 = 7
Row 6 = 8
Row 7 = 9

So we now have 9 people. There are 5 more people sitting in row n than row 2, and that's n - 2 (because our n = 7).

Hope that helps!

-t