contestada

Paul plans to put concrete on a rectangular portion of his driveway. The portion is 12 feet long and 6 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Paul needs is $108.89. Which of the following is closest to the width of the portion of the driveway on which Paul plans to put concrete? [1 foot = 12 inches; 1 yard = 3 feet] 3 feet 5 feet 8 feet 10 feet

Respuesta :

avachriss
We are given with the cost of concrete equal to $98 per cubic yard. Paul needs is $108.89. Hence the cubic yard is equal to  $108.89/ $98 per cubic yard or 1.1111 cubic yards. 1.1111 cubic yards is equal to 30.0024 cubic feet. From the given, 12 feet long length and 0.5 feet height, we get the width equal to 30.0024 cubic feet/12 feet/0.5 feet or 5 feet. The width needed is 5 feet.
JeanaShupp

Answer: 5 feet

Step-by-step explanation:

Let w be the width of portion.

Given: The length of the rectangular portion = 12 feet

We know that 1 yard = 3 feet

Then 1 feet = [tex]\dfrac{1}{3}\text{ yard}[/tex]

The length of the rectangular portion =  [tex]\dfrac{12}{3}=4\text{ yards}[/tex]

The height of the rectangular portion = 6 inches

1 yard = 36 inches

Then 1 inch = [tex]\dfrac{1}{36}\text{ yard}[/tex]

The height of the rectangular portion =  [tex]\dfrac{6}{36}=\dfrac{1}{6}\text{ yard}[/tex]

Now, the volume of the portion ( in cubic yards) :-

[tex]V=l\times w\times h = 4\times w\times\dfrac{1}{6}=\dfrac{2}{3}w[/tex]

The total cost of the concrete will be :-

[tex]98\times V=108.89\\\\\Rightarrow 98\times\dfrac{2}{3}w=108.89\\\\\Rightarrow\ w=\dfrac{108.89}{98\times\dfrac{2}{3}}=1.66668367347[/tex]

In feet , [tex]w=1.66668367347\times3=5.00005102041\approx5\text{feet}[/tex]

Hence, the width of the portion of the driveway on which Paul plans to put concrete is about 5 feet.