Question

Realtors use an index to compare housing prices in major cities. The housing price index values for several cities are given in the table below. Use the following formula to answer the question.

 price  (other town) = price  (your town) × index of other town  index in your town \underset{\text { (other town) }}{\text { price }}=\underset{\text { (your town) }}{\text { price }} \times \frac{\text { index of other town }}{\text { index in your town }}

 City  Index  City  Index  Atlanta 100 Las Vegas 115 Boston 146 Los Angeles 190 Chicago 105 Miami 161 Dallas 121 Phoenix 122 Denver 136 San Franciscol 172\begin{array}{lc|lc} \text { City } & \text { Index } & \text { City } & \text { Index } \\ \hline \text { Atlanta } & 100 & \text { Las Vegas } & 115 \\ \text { Boston } & 146 & \text { Los Angeles } & 190 \\ \text { Chicago } & 105 & \text { Miami } & 161 \\ \text { Dallas } & 121 & \text { Phoenix } & 122 \\ \text { Denver } & 136 & \text { San Franciscol } & 172 \end{array}

For a house valued at $600,000\$ 600,000 in Boston, find out the price of a comparable house in Los Angeles.

Solution

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Answered 1 year ago
Answered 1 year ago
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We can have the price of comparable house in Miami as:

Price Los Angeles=Price Boston×Index of Los AngelesIndex of Boston=$600,000×190146=$780,821.9178781,000\begin{aligned} \text{Price}_\text{ Los Angeles}&=\text{Price}_\text{ Boston}\times\frac{\text{Index of Los Angeles}}{\text{Index of Boston}}\\ &=\$600,000\times\frac{190}{146}\\ &=\$780,821.9178\\ &\approx781,000 \end{aligned}

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