A full jar of honey has a mass of 750g. After one third of the honey has been used up, the mass of the partly full jar is 550g. What is the mass of the empty jar.

There are several approaches.

Let the mass of the empty jar be {jatex options:inline}J{/jatex} and let the mas of the honey initially in the jar be {jatex options:inline}H{/jatex}. Then

{jatex options:inline}J+H=750 (1){/jatex}. When the jar is two thirds full the mass of the jar is 550g. Then

{jatex options:inline}J+\frac{2}{3}H=550{/jatex} (2)

2*(1)-3*(2) gives {jatex options:inline}-2(J+H)-3(J+\frac{2}{3}H)=2(759)-3(1650) \rightarrow -J=-150 \rightarrow J=150{/jatex}g.

Another approach is to say when one third of the honey is used, the mass drops by 200g, so the mass of the honey must initially be 600g. The mass of the jar is then 750-600=150g.