Answers:
- Person A receives at least 800 dollars, but no more than 1600 dollars
- Person B receives at least 1000 dollars, but no more than 2000 dollars
=============================================================
Explanation:
We don't have enough information to nail down exact figures, but we can make a range estimate.
The two people (call them A and B) share the profits in the ratio of 4 to 5
In shorthand notation, we can say the ratio is 4:5
This means person A gets 4x dollars while person B gets 5x dollars
The ratio 4x : 5x reduces to 4:5 after dividing both parts by x. The variable x is some positive real number.
The total profit is therefore 4x+5x = 9x dollars
This expression 9x is between 1800 and 3600 dollars, including both endpoints
We then can say...
[tex]1800 \le 9x \le 3600\\\\\frac{1800}{9} \le \frac{9x}{9} \le \frac{3600}{9}\\\\200 \le x \le 400[/tex]
We see that x = 200 is the smallest possible x value. This leads to person A and B receiving 4x = 4*200 = 800 dollars and 5x = 5*200 = 1000 dollars respectively. Note how the ratio 800:1000 reduces to 4:5 after we divide both parts by 200. We can see that 800+1000 = 1800 which is the lowest profit possible.
The inequality above shows that x = 400 is the largest x value possible. If this is the case, then person A receives 4x = 4*400 = 1600 dollars while person B receives 5x = 5*400 = 2000 dollars. The ratio 1600:2000 reduces to 4:5 after we divide both parts by 400. We can see that 1600+2000 = 3600 is the largest profit possible.
-------------------------
To summarize:
- Person A can receive anywhere between 800 dollars and 1600 dollars (inclusive of both endpoints).
- Person B can receive anywhere between 1000 dollars and 2000 dollars (inclusive of both endpoints).
The actual amount they receive will depend on what the actual profit is. Since we're only given the range of the profit, we can only make an estimated guess of the range for each partner.
-------------------------
Side note: For either person, the ratio of the max to min is 2:1. This tells us that the max amount they receive is double compared to the min amount they receive. It's no coincidence that 3600 is double that of 1800.
