I am stuck with this question... Can anyone help please:

Lisa's bucket does not have a hole in it and weighs 21kg when full of water. After she pours out half the water from the bucket, it weighs 12kg.

What is the weight of the empty bucket?

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- Jan 15th 2014, 02:39 AMNatasha1The weight of an empty bucket
I am stuck with this question... Can anyone help please:

**Lisa's bucket does not have a hole in it and weighs 21kg when full of water. After she pours out half the water from the bucket, it weighs 12kg.**

What is the weight of the empty bucket? - Jan 15th 2014, 02:53 AMREDnightRe: The weight of an empty bucket
im not sure with my answer but i think the answer is 3kg...

**her empty bucket weights 3kg...**

because when you subtract 12kg from 21kg the answer is 9kg...so 9kg is the half weight of the full water in her bucket...and when you multiply it by two the answer is 18kg...

then subtract 18kg from 21kg...so the answer is 3kg...

...im not sure with this...so forgive me if im wrong... - Jan 15th 2014, 03:37 AMREDnightRe: The weight of an empty bucket
hey!! im pretty sure with my answer...but its up to you if you wanna believe or not...

- Jan 15th 2014, 05:32 AMHallsofIvyRe: The weight of an empty bucket
Since it is the weight of the empty bucket we want to find, call that "x". Then the weight of water in it when it is full is 21- x. Half of that is (21- x)/2 and that is the weight of water in the bucket after half the water is poured out. So the weight of water

**and**bucket is now (21- x)/2+ x= (21- x)/2+ 2x/2= (21- x+ 2x)/2= (21+ x)/2= 12. Can you solve that equation? - Jan 15th 2014, 05:36 AMSorobanRe: The weight of an empty bucket
Hello, Natasha1!

Quote:

Lisa's bucket weighs 21kg when full of water.

After she pours out half the water from the bucket, it weighs 12kg.

What is the weight of the empty bucket?

REDnight, your reasoning is excellent!

"They" probably expected to see some Algebra.

Let $\displaystyle B$ = weight of the (empty) bucket.

Let $\displaystyle W$ = weight of the water (in a full bucket).

We have: .$\displaystyle B + W \:=\: 21\;\;[1]$

n . . . . . . $\displaystyle B + \tfrac{1}{2}W \:=\: 12\;\;[2]$

Subtract [1] - [2]: .$\displaystyle \tfrac{1}{2}W \:=\:9 \quad\Rightarrow\quad W \:=\:18$

Therefore: .$\displaystyle B \:=\:3$