Mass of quantities

Question

A bucket has a mass $12$ kg when it is filled with beans. When $\frac14$ full, it weighs $6$ kg. What is the mass of the bucket when empty?

Is this correct: Total mass of bucket = mass of beans + mass of empty bucket

$\frac14×12=3$
$6-3=3$
Mass of empty bucket $=3$ kg

Answer 1

The mass of the heap of beans that would fill $\frac34$ of the bucket is $12-6=6$ kg. Thus, the mass of the heap that would fill the whole bucket is $\frac43$ times this or $8$ kg, and the mass of the bucket alone is $12-8=4$ kg.

Answer 2

Let us solve this algebraically,

Suppose mass of beans= $m$ & mass of empty bucket is $b$. So according to problem $m+b = 12$

When we have $1/4$ beans then its mass is $\frac{m}{4}$.

So, $b + \frac{m }{4} = 6\Rightarrow 4b+m = 24$

Now its a simple problem of simultaneous equations, $m = 24-4b$.

Plugging this value in the first equation we get $24-4b+b=12$.

$\therefore 3b = 12 \Rightarrow {\boxed{\bf{b = 4}}}$,

So mass of the bucket alone is $\textbf{4}$ kg.