Question 1105376: Hi
all the orange juice in a carton was poured into 3 containers, A B C.20ml was poured from B to C and 210ml was then poured from C to A.150ml ws then poured out of A. As a result the amount of juice
In A in the end was 3 times the amount it had at first. B and C had the same amount left. This was 3 times the amount A had at the end.
How much juice was in each container at first.
thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! all the orange juice in a carton was poured into 3 containers, A B C.
everything is in milliliters.
container A contains x.
container B contains y.
container C contains z.
20 was poured from B to C.
container A contains x.
container B contains y - 20.
container C contains z + 20.
210 was poured from C to A.
container A contains x + 210.
container B contains y - 20.
container C contains z - 190 (Z + 20 - 210 = z - 190).
150 was then poured out of A.
container A contains x + 60 (x + 210 - 150 = x + 60).
container B contains y - 20.
container C contains z - 190.
As a result the amount of juice in A in the end was 3 times the amount it had at first.
x + 60 = 3x
B and C had the same amount left.
y - 20 = z - 190
This was 3 times the amount A had at the end.
y - 20 = 3 * (x + 60)
z - 190 = 3 * (x + 60)
How much juice was in each container at first?
from x + 60 = 3x, solve for x to get x = 30.
from y - 20 = 3 * (x + 60), solve for y as follows:
simplify to get y - 20 = 3x + 180
add 20 to both sides to get y = 3x + 200
replace x with 30 to get y = 90 + 200
solve for y to get y = 290.
from z - 190 = 3 * (x + 60), solve for z as follows:
simplify to get z - 190 = 3x + 180
add 190 to both sides to get z = 3x + 370
replace x with 30 to get z = 90 + 370
solve for z to get z = 460.
you have:
x = 30
y = 290
z = 460
go back and check the progression to make sure everything checks out ok.
everything is in milliliters.
start with:
A contains 30.
B contains 290.
C contains 460.
20 was poured from B to C.
A contains 30.
B contains 270.
C contains 480.
210 was poured from C to A.
A contains 240.
B contains 270.
C contains 270.
150 ml was then poured out of A.
A contains 90.
B contains 270.
C contains 270.
A now has 90 which is 3 * 30.
B contains the same amount as C which is 270.
the amount in B and C are each 270 which is 3 * 90 (90 is the ending amount in A).
everything checks out, so the solution is assumed to be good.
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