Question
A house was valued at \( \$ 239,000 \). Over several years, the value decreased by \( 7 \% \), giving the house a new value. \( \begin{array}{l}\text { (a) Fill in the blank to write the new value in terms of the old value. } \\ \text { Write your answer as a decimal. } \\ \text { New value }=\square \times \text { Old value } \\ \text { (b) Use your answer in part (a) to determine the new value. } \\ \text { New value: } \$ \square\end{array} \)
Ask by Daniel Todd. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Part (a):**
\[
\text{New value} = 0.93 \times \text{Old value}
\]
**Part (b):**
\[
\text{New value} = \$222{,}270
\]
Solution
Let's solve the problem step by step.
### Part (a)
When the value of the house decreases by \( 7\% \), it retains \( 100\% - 7\% = 93\% \) of its original value.
To express this as a decimal:
\[
93\% = 0.93
\]
**Answer:**
\[
\text{New value} = 0.93 \times \text{Old value}
\]
### Part (b)
Now, we'll calculate the new value using the original value of \$239,000.
\[
\text{New value} = 0.93 \times 239,000
\]
\[
\text{New value} = 222,270
\]
**Answer:**
\[
\text{New value} = \$222{,}270
\]
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Simplify this solution Extra Insights
To find the new value in terms of the old value after a \( 7\% \) decrease, we need to understand the reduction. If the house originally valued at \( \$ 239,000 \), a decrease of \( 7\% \) means it retains \( 100\% - 7\% = 93\% \) of its original value. In decimal form, that’s \( 0.93 \). So, the new value can be expressed as: New value = \( 0.93 \times \text{Old value} \). Now, applying it to find the actual new value: New value = \( 0.93 \times 239,000 = 222,570 \). Thus, the answers are: (a) New value = \( 0.93 \times \text{Old value} \) (b) New value: \( \$ 222,570 \)
