Question

5 a farmer wants to buy between 90 and 100 acres of land. - he is interested in a rectangular piece of land that is 1,500 yards long and 300 yards wide. - the piece of land is being sold as one complete unit for $87,000. if the farmer does not want to spend more than $900 an acre, does the land meet all of his requirements? (1 acre ≈ 43,560 ft²) a yes, the amount of land satisfies his needs, and the price is low enough. b no, the price is low enough, but there is too much land. c no, the price is low enough, but there is not enough land. d no, the amount of land satisfies what he needs, but the price is too high.

Explanation:

Step1: Calculate area of land in square yards

The land is rectangular with length \( l = 1500 \) yards and width \( w = 300 \) yards. The area \( A_{yd^2} \) of a rectangle is \( l\times w \). So, \( A_{yd^2}=1500\times300 = 450000\) square yards.

Step2: Convert square yards to square feet

Since 1 yard = 3 feet, 1 square yard = \( 3\times3 = 9\) square feet. So, to convert square yards to square feet, multiply by 9. \( A_{ft^2}=450000\times9 = 4050000\) square feet.

Step3: Convert square feet to acres

Given that 1 acre \( \approx 43560\) square feet. So, the area in acres \( A_{acres}=\frac{4050000}{43560}\approx92.97\) acres.

Step4: Check if acreage is within range

The farmer wants between 90 and 100 acres. \( 90 < 92.97 < 100\), so the acreage requirement is met.

Step5: Calculate cost per acre

The total cost is $87,000. Cost per acre \( C=\frac{87000}{92.97}\approx935.89\) dollars per acre.

Step6: Compare cost per acre with limit

The farmer does not want to spend more than $900 per acre. Since \( 935.89>900\), the cost requirement is not met.

Answer:

D. No, the amount of land satisfies what he needs, but the price is too high.