Question

Given a map of a garden in the scale of

1 cm = 4ft, find how much garden bark would
cost if you layer it 3 inches deep. Garden bark costs $5 a cubic yard.
The garden map showed approximately (rounded up) 40 square centimeters to be covered in bark. What is the cost?

Answer 1

(((3 × 40 × 7.62) 4) ÷ 3) × 5

120 × 7.62 × 4 ÷ 3 × 5

914.4 ÷ 4 (turn into feet) ÷ 3 (turn into cubic yards)

228.6 (now in feet) ÷ 3 × 5 (turn into dollars)

76.2 × 5

$381

Answer 2

$29.63

Explanation:

The given scale is 1 cm = 4 ft.

Therefore, the scale of square centimeters to square feet is:

`\sf (1\; cm)^2=(4\;ft)^2 \implies 1\;cm^2=16\; ft^2`

Given the garden map shows that approximately 40 cm² should be covered in bark, then the actual area to be covered in bark in square feet is:

`\sf 40 * 16\; ft^2=640\; ft^2`

As the depth of the bark is going to be 3 inches deep, and there are 12 inches in one foot:

`\sf 3\;in=(3)/(12)=(1)/(4)\; ft`

Therefore, the total volume of bark in cubic feet is:

`\sf Total\;volume=(1)/(4) \; ft * 640\; ft^2=160\;ft^3`

As 3 ft = 1 yd, then:

`\sf (3\;ft)^3=(1\;yd)^3 \implies 27\; ft^3=1\;yd^3`

Therefore, the total volume of bark in cubic yards can be found by dividing 160 ft³ by 27:

`\sf Total\;volume= (160)/(27)\; yd^3`

Given that the bark costs $5 per cubic yard, then the total cost of the bark is:

`\sf Cost\;of\;bark=(160)/(27) * \$5=\$29.63\; (2\;d.p.)`