Question

A farmer bought 100 ha of land, part at $1850 per hectare and part at $2250 paying for the whole $215000. How much land was there in each part? Do not round intermediate results. Round only final answers. Round to the whole. ha at $1850/ha ha at

Answer 1

`25` hectares were purchased at `$1850` and the remaining `75` hectares were purchased at `$2250`.

Explanation:

Let `x` be the number of hectares purchased for `$2250`. Since we know the total number of hectares purchased was `100`, this leaves `(100-x)` hectares remaining.

What you're trying to find is `x`. We know the total cost of the land was `$215,000`, so if you take the number of hectares purchased for `$2250` `(x)` and multiply it by the price `(2250)`, then add that to the remaining hectares that you know were purchased for `$1850`, you get the following equation:

`2250x + 1850*(100-x) = 215000`

`2250x + 185000 - 1850x = 215000 " "larr` Distribute the `1850`

`400x = 30000 " "larr` Combine like terms

`x = 75 " "larr` Divide by `400`

This means that the number of hectares purchased at `$2250` was `75` and the remaining number of hectares `(100-75 or 25)` was purchased at `1850`.