A bottle filled with juice weighs 8 pounds. One morning George drank 2/3 of the juice in the filled bottle. The bottle and the remaining juice weighed 3 pounds. What is the weight of the empty bottle, in pounds?

Question

texaschic101 · Answer

he drank 2/3 of the juice leaving 1/3
x = weight of the bottle
1/3 + x  = 3
3/3 + x = 8
hold on....it is not equaling...let me get someone

texaschic101 · Answer

@AccessDenied ...can you help.....this problem is messing with my brain

texaschic101 · Answer

@johnweldon1993 ...can you help...I don't even know if I am setting this up correctly

texaschic101 · Answer

@jim_thompson5910 ...can you help

texaschic101 · Answer

should I have done 2/3 of 8 for what he drank ?

texaschic101 · Answer

no...that doesn't make sense

jim_thompson5910 · Answer

let x = weight of the bottle (without any juice) and y = weight of juice alone (all of the juice)

we know that the bottle + juice originally is 8 lbs, so 

x+y = 8

solve for y to get

y = 8 - x

we also know that "George drank 2/3 of the juice in the filled bottle", so there's 1/3 of the juice left and this adds to the bottles weight (x) to get 3, so,

x + (1/3)y = 3

x + (1/3)(8 - x) = 3 ... plug in y = 8 - x

x + 8/3 - x/3 = 3

3x + 8 - x = 9 ... multiply every term by the LCD 3 to clear out the fractions

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...
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x = ???

texaschic101 · Answer

3x + 8 - x = 9
2x = 1
x = 1/2 
is it 1/2 a lb ?

jim_thompson5910 · Answer

yep, the bottle itself without any juice is 1/2 lb

texaschic101 · Answer

oh...I was way off

jim_thompson5910 · Answer

the juice alone is 8 - 1/2 = 15/2 = 7 1/2 = 7.5 lbs

jim_thompson5910 · Answer

check:

x+y = 8

0.5 + 7.5 = 8

8 = 8

works

------------------

x + (1/3)*y = 3

0.5 + (1/3)*7.5 = 3

0.5 + 2.5 = 3

3 = 3

works

texaschic101 · Answer

I see what you did....it makes more sense then what I was trying to do....you have saved me AGAIN. thank you

anonymous · Answer

Thank you so much. I was stuck on it for a while.

jim_thompson5910 · Answer

you're welcome, glad I could help

texaschic101 · Answer

he is good

anonymous · Answer

thank you for calling him and for your effort :)

texaschic101 · Answer

lol...I usually end up calling him when I am in a bind because I know he can help.

jim_thompson5910 · Answer

you did good texaschic101, you just needed that extra variable

texaschic101 · Answer

I always end up leaving something out :/

jim_thompson5910 · Answer

that's ok, that's what practice is for

anonymous · Answer

can you guys help me with one more question? I posted it up but no one answered it :(

jim_thompson5910 · Answer

sure

anonymous · Answer

thank you! let me close this