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 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?

Identify what to find: the original price of the car when it was new.
Name the unknown: Let $p$ = the original price.
Translate into a sentence and equation: "$12,000 is $\frac{3}{4}$ of the original price." This becomes the equation $12{,}000 = \frac{3}{4}p$ .
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, $\frac{4}{3} \cdot 12{,}000 = 16{,}000$ :

$16{,}000 = p$

Check by substituting back: Is $\frac{3}{4}$ of $16,000 equal to $12,000?

$\frac{3}{4} \cdot 16{,}000 \stackrel{?}{=} 12{,}000$

$12{,}000 = 12{,}000 \checkmark$

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 2026-04-21

Contributors are:

Who are from:

References

Learn Before

Related

Learn After