when a pail is 5/6 filled with sand, its mass is 1805g. When the same pail is 1/3 filled with sand, its mass is 917g. What is the mass of the empty pail?

Question

when a pail is 5/6 filled with sand, its mass is 1805g. When the same pail is 1/3 filled with sand, its mass is 917g. What is the mass of the empty pail?

Answer 1

Let P be the pail's mass in grams and let S be the Sand's mass (enough to fill pail). Then

 

P +(5/6)S = 1805

P + (2/6)S = 917   (1/3 full means 2/6 ratio)

 

You can subtract 2nd equation from 1st to et (3/6)S = 888 grams so S = 1776 grams. 

Then substitute into either equation, and solve for P.