Question

Kevin plans to put concrete on a rectangular portion of his driveway. The portion is 10 feet long and three inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Kevin needs is $72.59. Which of the following is closest to the width of the portion of the driveway on which Kevin plans to put concrete?

[1 foot = 12 inches; 1 yard = 3 feet]

3 feet

6 feet

8 feet

10 feet

Answer 1

Answer: 8 feet

Explanation:

The price of concrete is $98 per cubic yard.

1 cubic yard= $98

`\$1=(1)/(98)\ cu\ yard`

The total cost of the concrete Kevin needs is $72.59.

`\$72.59=(72.59)/(98)\ cu\ yard`....> Volume of concrete

In feet, the volume of the concrete =
`(72.59)/(98)*3*3*3=19.99928\approx20\ cu\ feet`

The volume of rectangular figure is given by :_

`Volume=length*width*height`

Length of concrete = 10 feet

, height of concrete = 3 inches=3/12 feet=1/4 feet

Let x be the width of the rectangular concrete, then the volume of the concrete is given by:-

`20=10*x*(1)/(4)\\\Rightarrow\ x=8\ feet`

Hence, the closest value for width f the portion of the driveway on which Kevin plans to put concrete=8 feet

Answer 2

The correct answer is 8 ft.

Explanation:
We start out by finding out the number of cubic feet of concrete used.
The cost of the concrete he used is $72.59. Since concrete is $98 per cubic yard, this means he uses less than 1 cubic yard. We divide 72.95/98 to find out what portion of a cubic yard he uses: 72.95/98 = 0.74 cu. yd.

Since the measurements of the driveway are given in feet and inches, we will change 0.74 cu. yd. to cubic feet. 1 cubic yard is a cube with length, width and height all 1 yd. 1 yd = 3ft, so the measurements of the cube are 3ft by 3ft by 3ft; this makes a volume of 27 cu. ft. We need 0.74 cu. yd. of concrete; 0.74*27 = 19.98 cu. ft.

We know that the volume of a rectangular prism is V=lwh. We have V=19.98, l=10, and h=3/12=0.25 (3 inches out of 12 inches it takes to make a foot). This leaves our width, w, unknown, and gives us the equation
19.98=10w(0.25).

Simplifying the right hand side gives us
19.98=2.5w.

Divide both sides by 2.5:
19.98/2.5 = 2.5w/2.5
7.992=w.

This rounds to 8 feet.