Concerning overall revenues and costs the school board estim

Concerning overall revenues and costs, the school board estimates that the revenues y (in millions of dollars) from state sources will decline according to the formula 4x+12y=180, and costs y (in millions of dollars) will increase according to the formula 6y-2x=70, where x is time (in years). After how many years will the costs equal the revenues?

Solution

the revenues y (in millions of dollars) from state sources will decline according to the formula 4x+12y=180

y = 180/12 - 4x/12

costs y (in millions of dollars) will increase according to the formula 6y-2x=70, where x is time (in years)

6y = 2x +70

y = 2x/6 +70/6

how many years will the costs equal the revenues:

180/12 - 4x/12 = 2x/6 +70/6

180/2 -4x/2 = 2x +70

90 -2x = 2x +70

4x = 20

x=5

After 5 years cost equal the revenues.