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

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Tony B Share
Feb 7, 2018

Answer:

The pail is 340 grams

Explanation:

#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"#

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Write your answer here...
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Answer

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Explanation

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1
Jan 6, 2017

Answer:

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:

#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

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