We are asked in this problem to look for the constant given the relationship of the variables is in inverse proportion.In this case, rainfall,r is inversely proportional to the water shortage,s. The expression that represents this is r = k/s where k is the constant of proportionality. Given the data on the problem, we substitute
r = k/s
40 in = k/ 200 million gal/d
using cross multiplication to find k, the resulting equation is
40 in * 200 million gal/d = k
8000 million gal in /d = k
8000 in scientific notation is 8x10^3 and million is 10^6, thus multiplying both is 8x10^9.
Thus k is equal to 8 x 10 ^9 with the units of gal in /d.
