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Surplus and Deficit Problems Calculator

Online surplus-and-deficit solver. Enter two allocation plans with their surplus and deficit to find the number of people and items, with reasoning—great for elementary word problems.

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People=(surplus+deficit)/rate difference; Items=rate×people+surplus
盈 12亏 6
Plan 1 rate
Left over
Plan 2 rate
Short by

📖 Tutorial | Surplus and Deficit

1. Definition
Two distributions, one with surplus and one short, determine people and items.
2. Formula & Notation
Surplus, deficitOver and short
Rate differenceBetween the plans
3. Properties & Laws
  • People=(surplus+deficit)/difference;
  • Items=rate×people+surplus;
  • Two surpluses use their difference;
  • Verify with plan 2.
4. Steps
  1. Enter rates a,b and surplus m, deficit n;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 8 leaves 12; 10 is 6 short.
Solution: people 9, items 84.
6. Common Pitfalls
One surplus, one deficit;
Plan 2 rate larger;
Non-negative.

❓ FAQ | Surplus and Deficit

Surplus-deficit?
Find people and items.
8/12,10/6?
9 people, 84 items.
Why the formula?
Extra per person totals surplus+deficit.
Two surpluses?
Use their difference.
Verify?
b×people−deficit.
Items?
a×people+surplus.