1Cademy - Translating Basic Percent Sentences to Equations

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Translating Basic Percent Sentences to Equations

Basic percent problems can be solved by translating English sentences directly into algebraic equations, rather than setting up proportions. Every basic percent sentence involves three quantities — the percent, the base (the whole amount), and the amount (the part of the whole) — and a typical problem supplies two of these while asking for the third. The same translation keywords used in general equation translation apply in percent contexts: the word "is" translates to an equals sign ( $=$ ), the word "of" translates to multiplication ( $\times$ ), and phrases like "what number" or "what percent" become a variable. It is helpful to choose a variable letter that serves as a reminder of the unknown (e.g., $n$ for "number" or $p$ for "percent"). Before placing the percent into the equation, it must be converted to its decimal form. This approach produces three standard equation types:

Finding the amount: "What number is $35\%$ of $90$ ?" translates to $n = 0.35 \times 90$ .
Finding the base: " $6.5\%$ of what number is $1.17$ ?" translates to $0.065 \times n = 1.17$ .
Finding the percent: " $144$ is what percent of $96$ ?" translates to $144 = p \times 96$ .

Once the equation is written, it is solved using the same properties of equality (multiplication, division) that apply to any linear equation with decimal coefficients. Many everyday situations — such as calculating tips, determining recommended daily nutrient amounts, or finding what fraction of calories comes from fat — reduce to one of these three equation types once the problem is translated into a single percent sentence.

Updated 2026-05-02

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