The population y in year x of Madison and Green Bay is approximated by the equations
Madison: -92x + 2y = 722
Green Bay: 3.87x + y = 558,
where x = 0 corresponds in 2000 and y in the thousands.
In what year do the two cities have the same population?
2007-12-11 12:30:33 · 4 answers · asked by Hillke 1 in Education & Reference ➔ Homework Help
Madison: -92x + 2y = 722
Green Bay: 3.87x + y = 558
equation 1: - 92x + 2y -722 = 0
equation 2: 3.87x + y - 558 = 0
y = 558 - 3.87x
substitute in equation1
-92x +2(558 - 3.87x) - 722 = 0
-92x + 1116 - 7.74x - 722 = 0
394 = 8.66x
45 = x
2045
2007-12-11 12:39:43 · answer #1 · answered by Steve A 7 · 0⤊ 0⤋
You want the year (x) where population (y) are equal. Then, set them equal to each other....
-92x + 2 y = 722
-46x + y = 361 divide both sides by 2 (coeffecient of y)
y = 46x + 361 rearrange...
3.87x + y = 558
y = -3.87x + 558 rearrange...
46x + 361 = -3.87x + 558
46x + 3.87x = 558 - 361
49.87x = 197
x = 197/49.87
x = 3.95
Since x=0 corresponds to year 2000, the actual year is 2000 + 3.95. Approximately year 2004
By the way, I am using slightly different method than the usual system of equations methods, but in principal, it IS the same thing. I set both equations equal to each other because you really don't care about the value of Y. You just want them equal to each other.
2007-12-11 20:43:13 · answer #2 · answered by tkquestion 7 · 0⤊ 0⤋
yes the guy above is right when he says you wont do these ever again....but they sure can help you not be an idiot....most people dont know how to do math.....so it is a good idea for your future to know how to do it.
system of equations....you have two unknowns and two equations.....
so solve for y in madison....y=361 + 46X
now sub for y in Green Bay 3.87x + 361+46x = 558
we then get 3.95...but we just round up because we cannot have the year 2003.95....thus the answer is 2004 and their populations will be....sub 4 into x and get y......Y=545.....or 545,000 people
2007-12-11 20:44:15 · answer #3 · answered by burg 1 · 0⤊ 0⤋
i remember these problems from High School. NEWSFLASH. after high school you will NEVER EVER EVER EVER need that again. UNLESS, you're going to be an architect. Other than that, you will NEVER EVER EVER use anything that you learned in highschool EVER again.
2007-12-11 20:34:52 · answer #4 · answered by Anonymous · 0⤊ 3⤋