Question

A farmer uses pesticides to keep harmful bugs away from his crops. the amount of pesticide used in an inverse variation of the percentage of bugs remaining on the crops. If he uses 5 gallons of pesticide per acre, 5% of the bugs remain. which equation describes this relationship? (let p denote the percentage of bugs and g denote the number of gallons used below.) a. p=1/4g b. p=4g c. p=1/4.g d. p=4/g

Answer 1

Option a p =
`(1)/(4g)`

Explanation:

It is given in the question, amount of pesticides used in an inverse variation of the percentage of bugs, remaining.

If p is the percentage of bugs and g is the gallons of pesticides used.

So p ∝
`(1)/(g)`

or p =
`(k)/(g)` where k is a constant.

Now it is given that p = 5 gallons per acre and g = 5% of the bugs.

5 =
`(k)/(0.05)`

k = 0.05 × 5 = 0.25

So equation will be

p =
`(k)/(g)`

or p =
`(0.25)/(g)` =
`(1)/(4g)`

Option a is the answer.

Answer 2

The inverse variation of the dimensions may be generally expressed as, x = k / y where k is the constant of indirect variation. Let x be the pesticides used (g) and y the percentage of the bugs remaining on the crops (p). Substituting the given to the equation,
5 = k / 0.05
The value of k is 0.25 or 1/4. Thus, the final answer is,
p = 1 / 4g