Chapter 3.5, Problem 8G

Last problem: A crop-dusting service is hired to spray a chemical pesticide over a field of broccoli, which I personally think tastes like feet, but some people seem to like. The plane has a 350-gallon tank that at the moment contains 80 gallons of a 0.5% solution, which means that 0.5% of the liquid in the tank is actually pesticide: The rest is water. The goal is to find how many gallons of a pre-mixed 1% solution would need to be added to increase the concentration in the tank to 0.8%.

a. How many gallons of pesticide are currently in the tank?

b. If we add x gallons of the 1% solution, how many gallons total will be in the tank?

c. If we’re adding x gallons of a 1% solution, how many gallons of pesticide are we adding? How many gallons of pesticide will we have total?

d. Now set up an equation that has two different expressions to describe the new amount of pesticide in the tank. One expression uses your answer to Question 8b, along with the fact that the new solution is 0.8% pesticide. The other expression is your answer to Question 8c. Then solve to find the number of gallons that would be needed to make the mixture 0.8% pesticide.

e. How many gallons of the 1% mix would we need to raise the concentration of the tank to 0.9%? Don’t start over from scratch! Just adapt your work from part c.