By Heather Lacey – Updated Aug 30, 2022
Algebra is a fundamental mathematical discipline that allows us to solve for unknowns. In everyday scenarios—from election turnout to payroll adjustments—knowing how to reverse‑calculate a total from a given percentage is essential.
A percentage is a shorthand for “per hundred.” For example, 2 % means 2 out of every 100 units.
Suppose you’re told that 2 % equals 80. Here, 2 % (the ratio 2/100) corresponds to the value 80.
Represent the unknown total with a variable, say x. The relationship can be written as:
\(\frac{2}{100}=\frac{80}{x}\)
Multiply the terms across the equals sign:
\(2x = 80 \times 100\)
which simplifies to:
\(2x = 8000\)
Divide both sides by 2:
\(x = \frac{8000}{2} = 4000\)
Substitute x = 4000 back into the original proportion to confirm that both sides equal 0.02.
Cross‑multiplication turns 2 % = 80 into 2x = 8000, yielding x = 4000. For any percentage p with value v, the total is \(\frac{v \times 100}{p}\).
Percentages can also be expressed as decimals (e.g., 2 % = 0.02). This method works for any situation where a percentage and its corresponding value are known.
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