Suppose that you want to find out how much gasoline is in an underground storage tank. You pour in 1 gallon of gasoline that contains some radioactive material with a long half-life that gives off 5500 counts per minute. The next day, you remove a gallon from the underground tank and measure its radioactivity to be 10 counts per minute.

1. How much gasoline is in the tank?

549 gallons

Explanation:

1 gallon of radioactive material was added to unknown volume of gasoline which we will represent as V in gallons.

Initially the 1 gallon gives a 5500 counts per minutes (cpm)

After adding to an underground gasoline tank, the total volume becomes

(V + 1) gallons

1 gallon was withdrawn from the underground and gave 10 cpm

using simple proportion and assuming the gasoline has mixed together

1 gallon gave 10 cpm

10 (V + 1) gallons should give 5500cpm

10 (V+1) = 5500cpm

divide both side by 10

V+1 = 5500 / 10 = 550

V = 550 - 1 = 549 gallons