P(n) = 20 + 0.10n
20 represents the $20 flat pay that Sagan receives weekly.
0.10 represents the $0.10 per subscriber that is added to Sagan's pay.
Q(n) = 30 + 0.05n
30 represents the $30 flat pay that the advertiser has offered to pay Sagan weekly.
0.05 represents the $0.05 per subscriber that the advertiser has offered to add to Sagan's pay.
If T(n) is the function representing Sagan's total weekly income, then
T(n) = P(n) + Q(n)
T(n) = 20 + 0.10n + 30 + 0.05n
T(n) = 50 + 0.15n
To find the number of subscribers that would make Sagan receive equal payments from the newspaper publisher and the advertiser, set the two functions equal to each other and solve for n.
P(n) = Q(n)
20 + 0.10n = 30 + 0.05n
20 + 0.10n + (-20) = 30 + 0.05n + (-20)
0.10n = 10 + 0.05n
0.10n + (-0.05n) = 10 + 0.05n + (-0.05n)
0.05n = 10
0.05n / 0.05 = 10 / 0.05
n = 200
Sagan would need 200 subscribers to be paid the same amount by both the publisher and the advertiser.