I posted this on puzzling stack exchange before I flagged it to delete it because I think it may be a pure mathematics question (it might take awhile before it's closed on puzzling stack exchange though). I also think the people here may be more inclined to answer this question.
https://puzzling.stackexchange.com/questions/87949/fated-to-earn-money
Here is my problem:
Joe has investments in Company A, Company B, and Company C.
Joe is fated to earn $25.00 from Company A within 2 days from now.
Joe is fated to earn $45.00 from Company B within 3 days from now.
Joe is fated to earn $100.00 from Company C within 5 days from now.
Joe is fated to earn no more than $26.00 from Company C and Company B on day 1 (1 day from now).
Joe is fated to earn at least $14.00 from Company A and Company C on day 2 (2 days from now).
Joe has to earn twice the amount of money on the first day than the second day from Companies A, B, and C and twice the amount of money on the second day than the third day from Companies A, B, and C. This can be expressed algebraically as Joe earning x money on day 3 (3 days from now), 2x money on day 2 (2 days from now), and 4x money on day 1 (1 day from now).
Joe can earn whatever amount of money (that satisfies the other conditions) from Companies A, B, and C on day 4 and day 5 (4 and 5 days from now).
What is the lowest amount of money Joe can earn on day 1 (1 day from now) from Companies A, B, and C? Explain your reasoning.
P.S. How come there doesn't seem to be good formulas to use for this question?
Edit: I do know the answer to this question, but I have no idea why. If you can explain your reasoning, that would be great!
Hint:
You won't have to calculate in cents for this question.