QuestionCalculate the total cost to pave a 2-mile, 20-foot-wide road at \$23.35 per linear foot.

Studdy Solution

STEP 1

Assumptions1. The length of the road to be paved is miles. . The width of the road is20 feet.
3. The cost of materials for each linear foot of the road is $23.35.
4. The cost is calculated based on the total area of the road to be paved.

STEP 2

First, we need to convert the length of the road from miles to feet, since the cost is given per linear foot. We know that1 mile is equal to5280 feet.
$Length\, in\, feet = Length\, in\, miles \\times5280$

STEP 3

Now, plug in the given value for the length in miles to calculate the length in feet.
$Length\, in\, feet =2\, miles \\times5280$

STEP 4

Calculate the length in feet.
$Length\, in\, feet =2 \\times5280 =10560\, feet$

STEP 5

Now that we have the length in feet, we can calculate the total area of the road to be paved. The area is given by the product of the length and the width.
$Area = Length\, in\, feet \\times Width\, in\, feet$

STEP 6

Plug in the values for the length and the width to calculate the area.
$Area =10560\, feet \\times20\, feet$

STEP 7

Calculate the area.
$Area =10560 \\times20 =211200\, square\, feet$

STEP 8

Now that we have the total area of the road to be paved, we can calculate the total cost of the materials. This is given by the product of the area and the cost per linear foot.
$Total\, cost = Area \\times Cost\, per\, linear\, foot$

STEP 9

Plug in the values for the area and the cost per linear foot to calculate the total cost.
$Total\, cost =211200\, square\, feet \\times \$23.35\, per\, linear\, foot$

STEP 10

Calculate the total cost.
$Total\, cost =211200 \\times23.35 = \$4,931,520$ The total cost of the materials needed to pave the road is $4,931,520.

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