# A pail, when holding 40 washers, weighs 500 grams. The same pail holding 20 washers weighs 420 grams. How much does the pail weigh?

340 grams

#### Explanation:

We have a pail and it holds various amounts of washers. How much does the pail weigh?

The total weight for any given amount of washers is:

$T W = \text{weight of pail"+"number of washers"xx"weight of one washer}$

We know that when there are 40 washers, the pail weighs 500 grams, and so:

$500 = \text{weight of pail"+"40"xx"weight of one washer}$

and we also know that when there are 20 washers the total weight is 420 grams:

$420 = \text{weight of pail"+"20"xx"weight of one washer}$

To make this easier to work with, I'm going to assign the variable $p$ to the pail and $w$ to the weight of one washer:

$500 = p + 40 w$
$420 = p + 20 w$

We can subtract the second equation from the first - that will allow us to find $w$ and from that we'll be able to find $p$:

$80 = 20 w$

$w = 4$

And let's substitute back in:

$500 = p + 40 w$

$500 = p + 40 \left(4\right)$

$500 = p + 160$

$p = 340$

I'll substitute back into the other equation as well to make sure we've got this right:

$420 = p + 20 w$

$420 = p + 20 \left(4\right)$

$420 = p + 80$

$p = 340$

That gives us the answer of:

$\left(p , w\right) = \left(340 , 4\right)$ with the answers in grams

Jan 7, 2017

The pail is 340 grams

#### Explanation:

$\textcolor{b l u e}{\text{Determine the weight of 20 washers}}$

$\textcolor{b r o w n}{\text{Subtraction gives:}}$

$\text{weight of "Pail +" weight of "40" washers" = 500" grams}$
$\underline{\text{weight of "Pail +" weight of "20" washers" = 420" grams}}$
" "0color(white)("--------------")+color(red)(" weight of "20" washers"=80" grams")

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the weight of the pail}}$

$\text{weight of "Pail+" weight of "20" washers" = 420" grams }$

$\text{weight of "Pail+" "color(red)(80" grams")" "=420" grams}$

Subtract 80 from both sides of the = gives

$\text{weight of "Pail = 340" grams}$