How to pro rate this?

Question

If 18,500 Units = $5,100  and 25,000 units = $4,350 what dollar amount does 23,000 units equal?

Answer 1

It's time to use either interpolate or extrapolate.

 

"Interpolation, in mathematics, the determination or estimation of the value of f(x), or a function of x, from certain known values of the function. If x₀ < … < x_n and y₀ = f(x₀),…, y_n = f(x_n) are known, and if x₀ < x < x_n, then the estimated value of f(x) is said to be an interpolation. If x < x₀ or x > x_n, the estimated value of f(x) is said to be an extrapolation." -- http://www.britannica.com/topic/interpolation

 

The problem gives the following points [ordered pairs (x,y)]:

    x            y

 18500     5100

 23000        x

 25000     4350

 

Using interpolation, we calculate how far 23000 is from 18500 and estimate that x is the same proportion of the way from 5100 to 4350.  Since we are assuming a straight line, we may find either "how far from" 18500 or "how far to" 25000 as long as we use the corresponding values of y.

 

(x-5100)/(4350-5100) = (23000-18500)/(25000-18500)

   [note that proportion may be set up multiple ways; y is decreasing, so negative slope]

 

(x-5100)/(-750) = 4500/6500

  6500x - 33150000 = -3375000             [cross multiply]

  6500x = 29775000                 [add 33150000 to both sides]

     x = 4580.769

 

The prorated value for 23,000 units is $4580.77

Answer 2

The ratios are not consistent.

 

18500/5100 = 3.627

 

25000/4350 = 5.74

 

Please check the original problem.