# 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

Apr 30, 2018

$25$ 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 $\left(100 - x\right)$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 $\left(x\right)$and multiply it by the price $\left(2250\right)$, then add that to the remaining hectares that you know were purchased for $1850, you get the following equation:

$2250 x + 1850 \cdot \left(100 - x\right) = 215000$

$2250 x + 185000 - 1850 x = 215000 \text{ } \leftarrow$ Distribute the $1850$

$400 x = 30000 \text{ } \leftarrow$ Combine like terms

$x = 75 \text{ } \leftarrow$ Divide by $400$

This means that the number of hectares purchased at $2250 was $75$and the remaining number of hectares $\left(100 - 75 \mathmr{and} 25\right)$was purchased at $1850\$.