Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

8000 acres

Explanation:

Let x represent the total acres of land owned by the farmer, i.e. x = total acres of land

Given that 90% of the total acres of land was cleared, we can state this as 90% of x = 0.9x

Therefore, land cleared for farming = 0.9x

Also, given that 40% of the land cleared was planted with Soybeans, we can represent this as 40% of 0.9x = 40/100(0.9x) = (40*0.9x)/100 = 36x/100 = 0.36x

Land cleared that was planted with Soybean = 0.36x

50% of the land cleared that was planted with wheat = 50% of 0.9x = 0.45x

If Soybean = 0.36x, wheat = 0.45x, and corn is said to be 720, land cleared (0.9x) by the farmer can be represented below as:

0.36x + 0.45x + 720 = 0.9x

We can solve to find the value of x, which represents the total acres owned by the farmer.

We have, 0.81x + 720 = 0.9x

0.81x – 0.9x = – 720

– 0.09x = – 720

x = 8000

Total acres owned owned by the farmer is 8000 acres.

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