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

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:

`TW="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="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="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+40w`
`420=p+20w`

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=20w`

`w=4`

And let's substitute back in:

`500=p+40w`

`500=p+40(4)`

`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+20w`

`420=p+20(4)`

`420=p+80`

`p=340`

That gives us the answer of:

`(p,w)=(340,4)` with the answers in grams

`color(blue)("Determine the weight of 20 washers")`

`color(brown)("Subtraction gives:")`

`"weight of "Pail +" weight of "40" washers" = 500" grams"`
`ul("weight of "Pail +" weight of "20" washers" = 420" grams")`
`" "0color(white)("--------------")+color(red)(" weight of "20" washers"=80" grams")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the weight of the pail")`

`"weight of "Pail+" weight of "20" washers" = 420" grams "`

`"weight of "Pail+" "color(red)(80" grams")" "=420" grams"`

Subtract 80 from both sides of the = gives

`"weight of "Pail = 340" grams"`