Question

Paul plans to put concrete on a rectangular portion of a driveway. The portion is 12 feet long and 6 inches high. The price of the concrete is $98.00 per cubic yard. The total cost of the concrete Paul needs is $108.89. What is the width of the driveway in feet which Paul plans to put concrete?

Answer 1

Answer:  5 ft

Step-by-step explanation:

Step 1: Find the volume of the driveway (in cubic yds)

$\ 108.89\div\dfrac{\ 98}{yds^3}=\ 108.89\times\dfrac{yds^3}{\ 98}=\boxed{\dfrac{10}{9}yds^3}$

Step 2: Use the Volume formula (V = length × width × heighth) to find w

(convert each measurement into yds)

$V=l\times w\times h\\\\\dfrac{10}{9}yds^3=12ft\bigg(\dfrac{1yd}{3ft}\bigg)\times w\times 6in\bigg(\dfrac{1ft}{12in}\bigg)\bigg(\dfrac{1yd}{3ft}\bigg)\\\\\\\dfrac{10}{9}yds^3=4yds\times w\times \dfrac{1}{6}yds\\\\\\\dfrac{10}{9}yds^3=\dfrac{2}{3}yds^2\times w\\\\\\\dfrac{3}{2yds^2}\times \dfrac{10}{9}yds^3=w\\\\\\\dfrac{5}{3}yds=w\\\\\\\dfrac{5}{3}yds\times\dfrac{3ft}{1yd}=w\\\\\\\large\boxed{5 ft=w}$