The Jeffersons are pouring a concrete driveway that is 36 feet long, 21 feet wide, and $\frac{1}{2}$ foot thick. a. We need to find the number of cubic feet of concrete needed. b. We need to convert the answer from part a to cubic yards using three unit multipliers.

1. Problem Description

The Jeffersons are pouring a concrete driveway that is 36 feet long, 21 feet wide, and $\frac{1}{2}$ foot thick.

a. We need to find the number of cubic feet of concrete needed.

b. We need to convert the answer from part a to cubic yards using three unit multipliers.

2. Solution Steps

a. To find the number of cubic feet of concrete, we need to calculate the volume of the driveway. The volume is given by the formula:

$Volume = Length \times Width \times Height$

Here, $Length = 36$ feet, $Width = 21$ feet, and $Height = \frac{1}{2}$ foot.

$Volume = 36 \times 21 \times \frac{1}{2} = 36 \times 21 \times 0.5 = 378$ cubic feet.

b. To convert cubic feet to cubic yards, we use the conversion factor 1 yard = 3 feet. Therefore, 1 cubic yard = $(3 \text{ feet})^3 = 27 \text{ cubic feet}$. We need to use three unit multipliers. The idea is to convert feet to yard three times.

$378 \text{ ft}^3 = 378 \text{ ft} \times \text{ft} \times \text{ft}$.

We use the conversion factor $\frac{1 \text{ yd}}{3 \text{ ft}}$ three times:

$378 \text{ ft}^3 \times \frac{1 \text{ yd}}{3 \text{ ft}} \times \frac{1 \text{ yd}}{3 \text{ ft}} \times \frac{1 \text{ yd}}{3 \text{ ft}} = 378 \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \text{ yd}^3 = \frac{378}{27} \text{ yd}^3 = 14 \text{ yd}^3$.

Alternatively, we can directly divide the cubic feet by 27 to get cubic yards:

$\text{Cubic yards} = \frac{\text{Cubic feet}}{27} = \frac{378}{27} = 14$ cubic yards.

3. Final Answer

a. The number of cubic feet of concrete needed is 378 cubic feet.

b. The number of cubic yards of concrete needed is 14 cubic yards.