Question

1. a farmer recently sold a large plot of land. the sale decreased his total acreage by 8%. let v be the original acreage.

a. find two equivalent expressions that will give the new acreage.
b. use the expressions to describe two ways to find the new acreage.

Explanation:

Part (a)

Step1: Analyze the decrease

The original acreage is \( v \). The decrease is \( 8\% \) of \( v \), which is \( 0.08v \) (since \( 8\%=\frac{8}{100} = 0.08\)).
To find the new acreage, we can subtract the decrease from the original acreage. So the first expression is \( v-0.08v \).

Step2: Simplify the expression

Simplify \( v - 0.08v \). We can factor out \( v \): \( v(1 - 0.08)=v\times0.92 = 0.92v \). So the second equivalent expression is \( 0.92v \).

Part (b)

• For the first way, we use the expression \( v - 0.08v \). Here, \( 0.08v \) is \( 8\% \) of the original acreage \( v \), and we subtract this decrease from the original acreage to get the new acreage.
• For the second way, we use the expression \( 0.92v \). Since the new acreage is \( 100\% - 8\%=92\% \) of the original acreage, we multiply the original acreage \( v \) by \( 0.92 \) (which is equivalent to \( 92\% \)) to get the new acreage.

Answer:

The two equivalent expressions are \( v - 0.08v \) and \( 0.92v \)