The city of Amanville has 6^2·7

Question

miles of roadway to maintain. Union Center has 6·7^3
miles of roadway. How many times more miles of roadway does Union Center have than Amanville? Round your answer to the nearest tenth if necessary.

times

Answer 1

To find how many times more miles of roadway Union Center has than Amanville, we first need to calculate the total miles of roadway for each city.

1. Amanville: \[ \text{Miles of roadway in Amanville} = 6^2 \cdot 7 \] Calculating \(6^2\): \[ 6^2 = 36 \] Thus, \[ \text{Miles of roadway in Amanville} = 36 \cdot 7 = 252 \text{ miles} \]

2. Union Center: \[ \text{Miles of roadway in Union Center} = 6 \cdot 7^3 \] Calculating \(7^3\): \[ 7^3 = 7 \cdot 7 \cdot 7 = 343 \] Thus, \[ \text{Miles of roadway in Union Center} = 6 \cdot 343 = 2058 \text{ miles} \]

3. Comparing the two: Now, we want to find how many times more miles of roadway Union Center has than Amanville: \[ \text{Ratio} = \frac{\text{Miles in Union Center}}{\text{Miles in Amanville}} = \frac{2058}{252} \]

   Performing the division: \[ \frac{2058}{252} \approx 8.16667 \]

   Rounding to the nearest tenth: \[ \text{Rounded ratio} \approx 8.2 \]

Therefore, Union Center has approximately 8.2 times more miles of roadway than Amanville.