How much does the empty jar weigh?

Question

A jar filled to 1/4 with jam weighs 250g. When the jar is 3/4 full, it weighs 350g. How much does the empty jar weigh?

Answer 1

1/4 full = 250 g, 3/4 full = 350 g

350 - 250 = 100 g = 3/4 - 1/4 = 1/2 full without the jar weight

1/2 full without the jar weight = 350-250 = 100 g

1/4 full without the jar weight = 50 g

3/4 full without the jar weight = 150 g

the jar weight = 250 - 50 -= 200 g

350-150 = 200 g = the jar's weight

Answer 2

Let R = jar

Let M = jam

R + 1/4M = 250

R + 3/4M = 350

Subtracting the top equation from the bottom equation

1/2M = 100

M = 200

Substituting,

R + 1/4(200) = 250

R + 50 = 250

R = 200g