Problem Solving - Joe is fated to earn cash

[Yukang]

Hi, I came up with a word problem that I know the answer to but I have no idea why the solution is what it is or how to reason through it. I posted this on another forum before, but I did not get the answer (explanation) I was looking for.

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?

 

[Deleted member 4993]

Hi, I came up with a word problem that I know the answer to but I have no idea why the solution is what it is or how to reason through it. I posted this on another forum before, but I did not get the answer (explanation) I was looking for.

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?

Please follow the rules of posting at this forum, enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.

Hint: This problem is more of "reading comprehension" than "formula application".

 

[Yukang]

I came up with the answer $44 through guess and check. Because the earnings are $26 for C & B on day 1, that leaves $18 for A on day 1 and 25-18=7 $7 dollars on day 2 for A. You want the contributions from Company C to be as low as possible so, $14 from C & A 2 days from now means the contributions from Company C is at least 14-7=7 $7. When setting the contributions for Company C in every other day to 0 until day 4 or 5, you get a total of $44 on day 1.

As for the subject topic, there is really no context other than general mathematics because I came up with the problem. The goal was to make a mathematical problem that didn't involve formulas or was difficult or impossible to reason through.

However, I don't know how to approach the problem the correct way through reasoning step by step. How would you find the answer to be $44 from a step by step analysis, not guess and check?