If a number, when divided by 4, is reduced by 21, the number is

### Concept & Logic Translating verbal relationships into a mathematical equation allows us to find the unknown value. Here, dividing by 4 equates to subtracting 21. $$ \frac{x}{4} = x - 21 $$ ### Step-by-Step Solution * Let the unknown number be $x$. * When the number is divided by 4, the result is $\frac{x}{4}$. * The problem states this new value is equal to the original number reduced by 21: $$ \frac{x}{4} = x - 21 $$ * Multiply the entire equation by 4 to eliminate the fraction: $$ x = 4(x - 21) $$ $$ x = 4x - 84 $$ * Rearrange the equation to solve for $x$: $$ 84 = 4x - x $$ $$ 3x = 84 $$ * Divide by 3: $$ x = \frac{84}{3} = 28 $$ ### Exam Strategy & Shortcut If dividing a number by 4 reduces it by 21, it means the removed portion represents $\frac{3}{4}$ of the original number. If $\frac{3}{4}$ of the number is 21, then $\frac{1}{4}$ of the number is $21 \div 3 = 7$. The whole number is $7 \times 4 = 28$. This logical deduction is much faster than writing out the algebraic steps. ### Common Pitfall Students might incorrectly translate "reduced by 21" as $21 - x$ instead of $x - 21$. Remember that reducing a value means subtracting from the original amount. ### Final Answer **Therefore, the correct answer is 28.**