Problems w/o solutions

Question

The sponsor of a time-share vacation condominium plans to sell the permanent use of an apartment for 50 weeks each year. Each week is designated to be either "prime" or "off-season." If each prime week sells for $7000 and each off-season week for $4000, and all weeks are sold, how many weeks must be prime in order for the sponsor to receive a total of $260,000 for the apartment? 

Answer 1

x = prime weeks

50 - x =off season weeks

 

260000 = 7000 x  +  (50 - x) 4000

260000 = 7000x + 200000 - 4000x

60000 = (7000-4000)x = 3000x

20 = x

 

20 prime weeks

30 off-season weeks