Linear Equation Word Problem Solution: Dooms Day Insurance:

Problem:

Dooms Day insurance charges a base fee plus a per dollar amount. For $3500, the company charges $189.50. For $5900, the company charges $297.50. How much would it charge for $12000?

Solution:

Think of coordinates: (3500, 189.5) and (5900, 297.5).

Find the slope of the line going through those points:

y2 - y1
x2 - x1

Plug in and solve:

297.5 - 189.5
5900 - 3500

=

 108 
2400

=

  9  
200

Now figure it out for 12000:

If you consider 12000 part of a coordinate, you will have (12000, y3) where y3 is the unknown.

We know the slope is 9/200. Since we are trying to determine y3 on the same line, we can use the same formula above that we used to calculate the slope, but this time with the 12000 and another value.

    y3 - 297.5    
12000 - 5900

=

  9  
200

Now, solve for y3:

y3 - 297.5
    6100

=

  9  
200

y3 - 297.5 = (9/200)(6100)

y3 - 297.5 = 274.5

y3 = 274.5 + 297.5 = 572

So, Dooms Day insurance charges $572 for $12000.

←