1Cademy - Solving a Word Problem for the Past Price of a Home

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Solving a Word Problem for the Past Price of a Home

Apply the seven-step problem-solving strategy to a real-world word problem to find a past price given a current price using multiplication and addition.

Problem: US Census data shows that the median price of a new home in the U.S. in November $2014$ was $\$280{,}900$ . This was $\$10{,}700$ more than $14$ times the price in November $1964$ . What was the median price of a new home in November $1964$ ?

Read the problem carefully. We are comparing a present house price to a past house price.
Identify what to find: the median price of a home in $1964$ .
Name the unknown: Let $p$ = the median price of a new home in $1964$ . The phrase " $\$10{,}700$ more than $14$ times the price in November $1964$ " translates to the algebraic expression $14p + 10{,}700$ .
Translate into an equation: The price in $2014$ was $\$280{,}900$ , so: $14p + 10{,}700 = 280{,}900$
Solve the equation. First, subtract $10{,}700$ from both sides: $14p = 270{,}200$ Divide both sides by $14$ : $p = 19{,}300$
Check: Is $\$10{,}700$ more than $14$ times $\$19{,}300$ equal to $\$280{,}900$ ? $14(19{,}300) + 10{,}700 \stackrel{?}{=} 280{,}900$ $270{,}200 + 10{,}700 \stackrel{?}{=} 280{,}900$ $280{,}900 = 280{,}900 \checkmark$
Answer: The median price of a new home in November $1964$ was $\$19{,}300$ .

This problem applies the two-step equation framework to real-world financial data, highlighting how "more than" translates to addition and "times" translates to multiplication.

Updated 2026-05-02

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OpenStax Intermediate Algebra

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