Question

1. a cement walk 3 ft wide is placed around the outside of a rectangular garden plot that is 20 ft by 30 ft. find the cost of the walk at $12.25 a square yard.

Explanation:

Step1: Find the outer - rectangle dimensions

The width of the garden is 20 ft and the length is 30 ft. The walk is 3 ft wide on each side. So the width of the outer - rectangle is \(20 + 2\times3=20 + 6 = 26\) ft and the length of the outer - rectangle is \(30+2\times3=30 + 6=36\) ft.

Step2: Calculate the area of the outer - rectangle and the garden

The area of a rectangle is \(A = l\times w\). The area of the outer - rectangle \(A_{1}=36\times26 = 936\) square feet. The area of the garden \(A_{2}=30\times20=600\) square feet.

Step3: Find the area of the walk

The area of the walk \(A = A_{1}-A_{2}=936 - 600=336\) square feet.

Step4: Convert square feet to square yards

Since 1 square yard = 9 square feet, the area of the walk in square yards is \(\frac{336}{9}=\frac{112}{3}\) square yards.

Step5: Calculate the cost of the walk

The cost per square yard is \( \$12.25=\frac{1225}{100}=\frac{49}{4}\) dollars. The total cost \(C=\frac{49}{4}\times\frac{112}{3}\).
\[

$$\begin{align*} C&=\frac{49\times112}{4\times3}\\ &=\frac{49\times28}{3}\\ &=\frac{1372}{3}\\ &\approx457.33 \end{align*}$$

\]

Answer:

\(\$457.33\)