algebra simultaneous question

[godemol]

The following is question #70 from OG 12th:

Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?

-the answer in the back of the book states that the total amount contributed can be deciphered as : $500 (n^2 +n). Please explain. Thanks.

[navalpike]

There are two separate rounds of donations.
First, mary persuaded n friends to donate $500 each.
Total amount = (n) 500
Then the n friends persuaded n more people to donate $500
Total amount = (n) (n) 500= 500 n^2
When we add the two amounts
500n^2 + 500n
500(n^2+n)

[truplayer256]

The key phrase in this question is, "EACH of these n friends persuaded n more people to donate $500 each to Mary's campaign." This means that 1 of Mary's friends persuaded n people and n of Mary's friends persuaded n*n or n^2 people. Everything else in this question is pretty simple and easy going.