A farmer recently sold a large plot of land. The sale decreased his total acreage by 10​%. Let x be the original acreage. Find two equivalent expressions that will give the new acreage. Use pencil and paper. Use the expressions to describe two ways to find the new acreage.

Answer 1

Let's find two equivalent expressions for the new acreage after selling 10% of the original acreage.

Method 1:
We know that the sale decreased the farmer's total acreage by 10%. In other words, the new acreage is 90% of the original acreage (100% - 10%). Therefore, the new acreage can be expressed as:
0.9x

Method 2:
We can also calculate the amount sold and subtract it from the original acreage to find the new acreage. Since 10% of the original acreage was sold, the amount sold is 0.1x. Subtracting this from the original acreage gives us:
x - 0.1x = 0.9x

So, the two equivalent expressions for the new acreage are 0.9x and x - 0.1x. Either of these expressions can be used to find the new acreage.