SOLUTION: Thanks so much for all the help!!! I have one last one that I think I have some clue about but not sure: A man is carrying rice on a journey. He passes through three custom stat

Question 170205: Thanks so much for all the help!!! I have one last one that I think I have some clue about but not sure:
A man is carrying rice on a journey. He passes through three custom stations. At the first he gives up 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; at the third he gives up 1/4 of what remains. After passing through all three custom stations, he has 6 pounds less than he started with. How much rice did he have when he started?
Found 2 solutions by scott8148, jim_thompson5910:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
follow how much the man keeps __ let x=starting amount

"At the first, he gives up 1/3 of his rice" __ keeps (2/3)x

"at the second he is allowed to keep 1/3 of what is left" __ keeps 1/3 of (2/3)x __ now has (2/9)x

"at the third, he gives up 1/4 of what remains" __ keeps 3/4 of (2/9)x __ now has (1/6)x

"At the end, he has 6 pounds less than what he started with" __ (1/6)x=x-6

multiplying by 6 __ x=6x-36

adding 36-x __ 36=5x

dividing by 5 __ 7.2=x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=amount of rice he starts with and y=amount he has leftover

After First Station

Since "At the first he gives up 1/3 of his rice", this tells us that after the first station, he has pounds of rice leftover

Note: I've subtracted 1/3 of the amount "x" from "x"

Combine like terms to get . So he has pounds of rice leftover after the first station (this makes sense because the guard took 1/3 so the man must have 2/3 leftover).

Note: remember, the "x" is just a number (a number in which we do NOT know). However, to help you get an idea of what is going on, let (ie let's say that he started at 12 lbs of rice). After the first station, he would have lbs of rice.

--------------------------------------------

After Second Station

Keep in mind that the man still has lbs of rice.

Since at "the second he is allowed to keep 1/3 of what is left", this means that they will take 2/3 of what he has left.

So this means that you need to subtract like this

Amount he has left - (2/3)*(Amount he has left )

Multiply

Combine the fractions.

So after the second station, he has lbs of rice left.
--------------------------------------------

After Third Station

Finally, because "at the third he gives up 1/4 of what remains", this tells us that we subtract 1/4 of what he has left like this:

Amount he has left - (1/4)*(Amount he has left )

Which algebraically looks like:

Multiply

Combine the fractions.

So after the third station, he has lbs of rice left.

----------------------------------------------------------

Since "he has 6 pounds less than he started with." this means that he ended up with lbs. Also, we know that he ended up with lbs of rice (after passing through the third station)

So this means that the two are equal, so...

Multiply EVERY term by the LCD 6 to clear the fraction.

Add to both sides.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Divide.

=============================================================

Answer:

So the man started with 7.2 lbs of rice and the amounts after each station are:

1st station: so he had 4.8 lbs after the 1st station

2nd station: so he had 1.6 lbs after the 2nd station

3rd station: so he had 1.2 lbs after the 3rd station

Since the difference between 7.2 and 1.2 is this helps confirm our answer.

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