Math

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

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  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)

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  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.

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