Question

A developer estimates that 1/5 of land just purchased is not physically suitable for any use and 5% of the land must be used for roads. If the remaining amount of land totals 90 acres, how many total acres were purchased?

A. 100 acres
B. 112.5 acres
C. 120 acres
D. 95 acres

Answer 1

By setting up an equation to represent the land suitable for use and the land reserved for roads and unsuitable land, we find that the total amount of land purchased is 120 acres.

Step-by-step explanation:

To calculate the total amount of land purchased, we have to consider the usable land plus the portions allocated for other uses. We know that 1/5 of the land is not suitable for use, and an additional 5% is reserved for roads. The remaining usable land accounts for 90 acres. We can represent the total land with the variable x.

The equation representing this situation is: (4/5)x (usable land after unfit portion is subtracted) minus 0.05x (land for roads) equals 90 acres.

Combining the terms, we have (4/5)x - 0.05x = 90. To find x, we can solve this equation:

• First, we convert 5% to a decimal, which is 0.05.
• The equation is now (0.8x - 0.05x) = 90.
• Combining like terms gives us 0.75x = 90.
• Dividing both sides of the equation by 0.75 gives us x = 120.

Therefore, the total amount of land purchased is 120 acres.