Moisture content and mass balance: Fresh grapes are 80% water and dry grapes are 10% water. If the weight of dry grapes is 500 kg, what would be the equivalent weight when fresh?

Introduction / Context:
Moisture problems are solved via mass balance on solids because the solid portion remains constant when water content changes. Here we convert a dry batch to its fresh equivalent using solid fractions.

Given Data / Assumptions:

• Fresh grapes: 80% water ⇒ 20% solids.
• Dry grapes: 10% water ⇒ 90% solids.
• Dry-grape batch weight = 500 kg.
• Solids are unchanged between states.

Concept / Approach:
Compute solid mass in the dry batch (90% of 500 kg). Then equate this to solid mass in the fresh state (20% of fresh weight). Solve for fresh weight by dividing by the fresh solid fraction.

Step-by-Step Solution:
Dry solids = 0.90 * 500 = 450 kgFresh solids fraction = 0.20Fresh weight = 450 / 0.20 = 2250 kg

Verification / Alternative check:
Reverse check: 20% of 2250 is 450 kg solids; converting to dry (90% solids) gives 450/0.90 = 500 kg. Consistent.

Why Other Options Are Wrong:
2350, 2085, 2555, 2000 do not preserve the solids at 450 kg when converted back and forth between 20% and 90% solids states.

Common Pitfalls:
Comparing water weights directly instead of conserving solids; or mistakenly applying percent to the wrong base (total vs solids).

Final Answer:
2250 kg