Question 124751
The present value (V) of the computer is equal to the original cost (C) less the depreciation (D).
So you can start by writing:
{{{V = C-D}}}
But, you are to assume that the depreciation (D) is a linear function of (directly proportional to) the number of months of use (t).  So the depreciation (D) can be expressed as:
{{{D = kt}}} where k is the constant of proportionality. You can find the value of k as follows:
First, rewrite the equation for the value V in terms of the months of use, t, by replacing D with kt, as:
a) {{{V = C-kt}}} You can write two equations, one for each of the given depreciation values and months of use.
{{{V[1] = C-kt[1]}}}
{{{V[2] = C-kt[2]}}}
Now substitute the given values of {{{V[1] = 890}}}, {{{t[1] = 8}}}, {{{V[2] = 750}}}, and {{{t[2] = 10}}} to get the two equations:
1) {{{890 = C-k*(8)}}} Rewrite this as:{{{C = 890+8*k}}}
2) {{{750 = C-k*(10)}}} Rewrite this as:{{{C = 750+10*k}}}
Now set these two equations equal to each other to get:
{{{890+8*k = 750+10*k}}} Simplify and solve for k. Subtract 750 from both sides.
{{{140+8*k = 10*k}}} Subtract 8*k from both sides.
{{{140 = 2*k}}} Divide both sides by 2.
{{{k = 70}}}
b) Now you can find the original cost of the computer.
{{{C = 890+8*k}}} Substitute k = 70.
{{{C = 890+8*70}}}
{{{C = 890+560}}}
{{{C = 1450}}} or...
{{{C = 750+10*k}}}
{{{C = 750+10*70}}}
{{{C = 750+700}}}
{{{C = 1450}}}
The original cost of the computer is $1,450.00

The monthly depreciation is just the value, k, or $70.00 per month.
Or you can calculate it as:
{{{(C-D[1])/t[1] = (1450-890)/8}}} ={{{560/8 = 70}}} or...
{{{(C-D[2])/t[2] = (1450-750)/10}}}={{{700/10 = 70}}}