Fraction word problem

Question

A crate of cans of paint weighs 240lbs when it is 3/4 full. It's weighs 102lbs when it is 3/10 full. What is the weight of the crate?

Answer 1

if the weights given consist of the cans of paint and the crate, then we can set up 2 equations.

 

X = total weight of paint cans (crate is full)

C = weight of Crate

 

#1)     (3/4) X + C  = 240 lbs

#2)   (3/10) X + C = 102 lbs

 

subtract the 2nd equation from the 1st

 

 (3/4 - 3/10) X  = 138        (15/20 - 6/20) = 9/20

 9/20 X  = 138

 

X = 306.6667     (4 decimals)   TOTAL WT OF FULL CRATE OF PAINT

 

now just substitute in either equation above.  I'll use eqn #1 above

 

(3/4) 306.6667 + C = 240    (Solve for C)

C = 240 - 230  or  C (crate) = 10 lbs

 

we can check this with the 2nd eqn. 

 

(3/10) 306.6667 + 10 = 102 lbs  ???

                    92 + 10 = 102        (checks)