SOLUTION: Sir Please help me to sovle the following question. The number of nursing homes in Massachusetts between 1993 and 1997 can be describe by m(x) =3.37x – 6212.34 and the number

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Sir Please help me to sovle the following question. The number of nursing homes in Massachusetts between 1993 and 1997 can be describe by m(x) =3.37x – 6212.34 and the number      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 828217: Sir Please help me to sovle the following question.
The number of nursing homes in Massachusetts between 1993 and 1997 can be describe by
m(x) =3.37x – 6212.34
and the number of nursing homes at the same time in Illinois is given by
n(x) = 12.34x – 23802.09
In each equation, x is represents the year (Source: Health Care Financing Administration)
a) Assuming that the pattern indicated by these equations is valid prior to 1993, during what year did Massachusetts and Illinois have same number if nursing homes?
b) How many homes were there in each state when the numbers of nursing home were equal?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
At some time x, the number of nursing home is the same in both sates. We will call that number y
system%28y=3.37x-6212.34%2Cy=12.34x-23802.09%29 --> system%28y=3.37x-6212.34%2C3.37x-6212.34=12.34x-23802.09%29 --> system%28y=3.37x-6212.34%2C23802.09-6212.34=12.34x-3.37x%29 --> system%28y=3.37x-6212.34%2C17589.75=8.97x+%29 --> system%28y=3.37x-6212.34%2Cx=17589.75%2F8.97%29 --> system%28y=3.37%2A1960.95-6212.34%2Cx=1960.95%29 --> highlight%28system%28y=396%2Cx=1961%29%29 (rounding)