This is the (average) sale price for single family property in Seattle and Port Townsend

Question

Year Seattle Port Townsend
1970 $38000 $8400
1990 $175000 $168400
(a) When will the average sales price in seattle and port t. be equal and what is this price?
(b)When will the average sales price in port t. be $15000 less than seattle sales price? What are the two sales prices at this time?

I need help setting up the equations for these two questions.
i found the linear model relating to this question
seattle is :
y=6850(x-1970)+38000
port t:
y=7980(x-1970)+8400

Answer 1

The linear equations are:

seattle: y=6580(x-1970)+38000

port t: y=8000(x-1970)+8400 <---you made an arithmetic error in calculating the slope for this one

1. To find when they will be equal just set the to equations equal to each other:

6580(x-1970)+38000=8000(x-1970)+8400
6580x-12962600+3800=8000x-15760000+8400
2792800=1420x
x=1966.76

1966

2. Here you just take the port t equation, add 15000, and set that equal to the seattle equation

so
8000(x-1970)+8400+15000=6580(x-1970)+38000
do the algebra and you get: 1980.28
so 1980

the second part ask for the two sales prices during this time, so just plug our answer, 1980, back into the equations:

seattle: y=6580([1980.28-1970)+38000, y= $105,642.4
port t: y=y=8000(1980.28-1970)+8400, y= $90640
we can then check our answer by doing 105,642-90640=15002 which confirms that seattle at this time is 15000 more than port t. (the number is a tiny bit off because 1980.28 is rounded)

Answer 2

Thanks for helping. What you explained to me makes sense. But i checked the back of the book and it said for (a) they will be equal in 1995 at $214,313.
so is (b) it said its 1982.70 Sea=$124,965. weird...
I going to try these problems out! and see what answers I get! thanks again.