Thread: Algebraic Word Translations

Hi All.

'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' Denote a formula for the amount contributed to the campaign.

Translating this I would work as follows.

1. Mary persuaded n friends to dontate $500 each to her election campaign: [tex]500n[\MATH]
2. Each of these n friends persuaded n more people to donate $500 each to Mary's campaign[tex]500n(500n)[\MATH]

However the answer is [tex]$500(n^2 + n)[\MATH]

Where did I go wrong?

Thanks,
D

try thinking like this:

how much do mary's friends donate
this is number of people * donation
number of people: n
donation: 500

amount: 500n

how much do their friends donate
number of people: n*n
donation: 500

Amount = 500n^2


so the total donated is:
500n + 500n^2 = 500(n^2 + n)

there are n people, not 500n people. Your first "500n" is the amount of money.

If each of n people contacts another n people, then they will have contacted people, which,together with the original n, makes n^2+ n people, each of whom contributes $500.