what is the mass

Question

A bottle has a mass of 1.8 kilograms when it is completely filled with juice. It has a mass of 1.23 kilograms when 3/8 of the juice is removed. What is the mass of the empty bottle

Answer 1

let B is the mass of the bottle empty

let J is the mass of the juice alone

 

B+J = 1.8

 

B+5/8J=1.23

 

subtract both equations and you get

j-3/8j=1.8-1.23

 

3/8j=.57

 

=8(.57)/3=J

 

j=1.52

 

substitute j into one of the equations above to find B

 

B+1.52=1.8

B=1.8-1.52

B=.28KG

 

 

Answer 2

Let B be the weight of the bottle

J is the weight of juice that will fill the bottle.  

 

When the bottle is completely full of juice, the weight of bottle is J+B

 

When 3/8 of the juice is removed, 5/8 of the bottle is filled with juice.  Then the weight of the juice is 5/8J and the weight of the bottle with the juice is B+5/8J

 

We are given that 1.8kg = J+B = mass of full bottle

1.23kg = 5/8J+B = mass of bottle with 5/8 juice.

 

From first equation we have: J=1.8-B

Subsitute into second:

 

1.23 = 5/8*(1.8 - B) + B

1.23 = 5/8*1.8 - 5/8B + B = 1.125 +3/8B

1.23 - 1.125 = 0.105 = 3/8B

B = 0.105 * 8 / 3 = 0.28kg