SOLUTION: Mari and James are friends. The difference between 9 times James' age and 4 times Mari's age is 72. Twelve years ago, James was half as old as Mari was. a) Write a linear syst

Question 440130: Mari and James are friends. The difference between 9 times James' age and 4 times Mari's age is 72. Twelve years ago, James was half as old as Mari was.
a) Write a linear system to describe the relationship between Mari's age and James age.
b) Graph the system on a grid
c) Five years from now, how old will Mari and James be?

I'm getting stumped on A&B. I thought that a) would be 9x-4y=72, and b) would be j-12=1/2(y-12), but the two aren't intersecting, so I must be thinking the equation incorrectly!
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Assuming that you meant the second equation to be x-12=1/2(y-12), the equations look right to me. When I solved the system that you have, I got James=24 and Mari=36 years present age. Of course in 5 years they will be 5 years older so the answer to the question should be J+5=29 and M+5=41. You mentioned that you were solving this system by graphing, and you said the lines did not intersect! Maybe you did not extend the graph far enough. You will need a LARGE graph to contain the point (24,36).

Here is the graph of the two lines. If you are using a graphing calculator, like the one in algebra.com, you will need to solve for y in each of the equations. Then most importantly, be sure to make the window of the calculator large enough. I'm using x and y from -10 to 50 .

a) 9x-4y=72
-4y = -9x + 72
y=(9x-72)/4

b) x-12=1/2(y-12)
2(x-12)=y-12
y=2(x-12) + 12

As you can see, the lines DO actually intersect!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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