Question

A environmental initiative has the goal of saving at least 25 2525 million hectares of rainforest through both planting trees and purchasing land. The cost of planting trees is $ 400 $400dollar sign, 400 per hectare, and the cost of purchasing land is $ 260 $260dollar sign, 260 per hectare. If the initiative has a budget of $ 8 , 250 $8,250dollar sign, 8, comma, 250 million, which of the following is a possible way for the initiative to accomplish its goal without exceeding its budget?

Answer 1

Answer:

The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.

Step-by-step explanation:

Let the variable X represent the amount of land used for planting trees and Y represent the amount of land purchased.

The goal of the environmental initiative is to save at least 25 million hectares of rain forest.

That is:

X + Y = 25....(i)

Now it is provided that:

• The cost of planting trees is $ 400 per hectare.
• The cost of purchasing land is $ 260 per hectare.
• The initiative has a budget of $8,250 million.

Using the above data it can be said that:

400X + 260Y = 8250....(ii)

Solve equations (i) and (ii) simultaneously.

$\ \ \ \ x+y=25]\times 260\\400x+260y=8250\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\\Rightarrow\\\\260x+260y=6500\\400x+260y=8250\\(-)\_\_\_\_\_\ (-)\_\_\_\_(-)\_\_\_\\\\\Rightarrow\\\\-140x=-1750\\\\x=\frac{1750}{140}\\\\x=12.5$

Then the value of y is:

$x+y=25\\y=25-x\\y=25-12.5\\y=12.5$

Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.