Question

1. you estimate the cost of seeding a 150 m by 210 m area with seed. you need 3 pounds of seed per 100 000 square feet. how many pounds of seed will you need?

Explanation:

Step1: Calculate the area in square meters

The area of a rectangle is length times width. So, the area \( A \) of the field is \( 150 \, \text{m} \times 210 \, \text{m} \).
\( A = 150 \times 210 = 31500 \, \text{m}^2 \)

Step2: Convert square meters to square feet

We know that \( 1 \, \text{m} = 3.28084 \, \text{ft} \), so \( 1 \, \text{m}^2 = (3.28084)^2 \, \text{ft}^2 \approx 10.7639 \, \text{ft}^2 \).
To convert \( 31500 \, \text{m}^2 \) to square feet, we multiply by \( 10.7639 \):
\( 31500 \times 10.7639 \approx 31500 \times 10.764 = 31500 \times 10 + 31500 \times 0.764 = 315000 + 24066 = 339066 \, \text{ft}^2 \) (approximate)

Step3: Calculate the amount of seed needed

We need 3 pounds of seed per 100000 square feet. Let \( x \) be the amount of seed needed (in pounds).
We set up a proportion: \( \frac{3 \, \text{pounds}}{100000 \, \text{ft}^2} = \frac{x}{339066 \, \text{ft}^2} \)
Cross - multiplying gives \( x=\frac{3\times339066}{100000} \)
\( x = \frac{1017198}{100000}=10.17198\approx10.17 \) pounds

Answer:

Approximately \( 10.17 \) pounds of seed will be needed.