Natalie purchases a new car for $26,868. She pays 3,000 up front and agrees to make a $430 payment every month for 60 month Natalie’s car loses value as it get older. A common accounting method to track this loss of the value is straight-line depreciation. According to straight-line depreciation, Natalie’s car loses $223 in value each month After how many months will the money Natalie had paid equal the value of her car?

It will take 36.6 or 37 months.

We will set up an equation to represent this.  Let m be the number of months.  The amount of money she has paid can be represented by 3000+430m.  The amount of money her car is worth can be represented by 26868-223m.  Set these equal:

3000+430m=26868-223m

Add 223m to both sides:
3000+430m+223m = 26868-223m+223m
3000+653m=26868

Subtract 3000 from both sides:
3000+653m-3000 = 26868-3000
653m=23868

Divide both sides by 653:
653m/653 = 23868/653
m = 36.6