Barrel riddle...?

Question

Hello, thanks for taking the time to read/help.

Here is the problem I'm having trouble with...

A barrel of honey weighs 50 pounds. The same barrel with Kerosene in it weighs 35 pounds. If honey is twice as heavy as Kerosene, what is the weight of the empty barrel?

Answer 1

let the weight of the empty barrel be x pounds
x+k=35 pounds
x+2k=50 pounds
subtracting
k=15
substituting x=20 pounds
weight of the barrel=20 pounds

Answer 2

Let B be the weight of the barrel, H the weight of the honey and K the weight of the kerosene.

Then we have B + H = 50, B + K = 35, H = 2K.
Put H = 2K into the first equation to get
B + 2K = 50
B + K = 35
and subtract these to get
K = 15.
Then B + K = 35 => B = 20 (and H = 2K => H = 30).
So the barrel weighs 20 pounds.

Answer 3

let a be the weight of Kerosene
let b be the weight of empty barrel

we have
2a + b =50
a + b = 35

=> a = 15 b = 20
so empty barrel weighs 20 pounds

Answer 4

Let

b = weight of empty barrel
h = weight of honey
k = weight of kerosene

b + h = 50
b + k = 35
h = 2k

Subtracting

h - k = 50 - 35 = 15
2k - k = 15
k = 15

b + k = 35
b + 15 = 35
b = 20 lbs

Answer 5

Label the barrels making use of ten binary digits. you're able to do 1024 barrels this way, yet it extremely is effective, you in basic terms brush aside the extra suitable 24 opportunities. Assign each and each slave a digit place, and provide him a tumbler with extremely wine from each and each barrel the place his digit place is a one million. they might then all drink their glasses on the comparable time. to jot down down the respond, for each slave that dies, write a one million in his digit place, and for each slave that continues to be alive, placed a 0 in his digit place. The ensuing written binary variety will come across the poisoned barrel.

Answer 6

X = barrel
y = kerosene

2y + x = 50
y+ x = 35

-x - y = -35

y = 15
x = 20

Barrel is 20 pounds