1Cademy - Solving a Word Problem for a Cars Original Price

Learn Before

Problem-Solving Strategy for Word Problems

Example

Solving a Word Problem for a Car's Original Price

Apply the seven-step problem-solving strategy to find an original price when only a fractional portion of it is known, using the Multiplication Property of Equality. Problem: Andreas purchased a used car for $12,000. Since the car was 4 years old, this price was $\frac{3}{4}$ of the original price when it was new. What was the original price of the car? 1. Read the problem carefully to understand the relationship between the known and unknown values. 2. Identify what to find: the original price of the car when it was new. 3. Name the unknown: Let $p$ = the original price. 4. Translate into a sentence and equation: The amount $12,000 is $\frac{3}{4}$ of the original price. This becomes the equation $12{,}000 = \frac{3}{4}p$ . 5. Solve by multiplying both sides by $\frac{4}{3}$ , the reciprocal of the fractional coefficient $\frac{3}{4}$ : $\frac{4}{3}(12{,}000) = \frac{4}{3} \cdot \frac{3}{4}p$ On the right side, $\frac{4}{3} \cdot \frac{3}{4} = 1$ by the inverse property of multiplication, leaving just $p$ . On the left side, $\frac{4}{3} \cdot 12{,}000 = 16{,}000$ : $16{,}000 = p$ 6. Check by substituting back: Is $\frac{3}{4}$ of $16,000 equal to $12,000? $\frac{3}{4} \cdot 16{,}000 \stackrel{?}{=} 12{,}000$ 12{,}000 = 12{,}000 checkmark 7. Answer: The original price of the car was $16,000. This example illustrates how the phrase "fraction of a quantity" translates into multiplication by that fraction. When the known value equals a fraction times the unknown, the equation takes the form $\text{known} = \frac{a}{b} \cdot p$ , and the unknown is isolated by multiplying both sides by the reciprocal $\frac{b}{a}$ . This pattern arises frequently in real-world problems involving discounts, depreciation, or partial quantities.

Updated 2026-06-27

Contributors are:

Who are from:

References

Learn Before

Related

Learn After