You need an arithmetical formula to solve with.
I know this is probably elementary for the users of this site, but I have a problem that I am struggling to even find an equation for, let alone the solution. Here is the problem:
You have $135,245,210. How many items can you purchase if they cost $221,400 and their price increases by $1800 with each item purchased?
It's been quite some time since I've done any Algebra, and I cannot even come up with the equation to find the solution. So any help would be much appreciated. Thanks!
Check out this site: Mathwords: Arithmetic Sequence
Essentially correct. Keep in mind that you're increasing n step by step so you need another shortcut formula (a summation formula) which is at
Mathwords: Arithmetic Series
OK, here we go; formula for sum of series is:
[number of terms] * [(first term + last term) / 2]
n = number of terms = ?
a = 1st term = 221400
f = last term = 221400 + 1800(n-1) : YES, n-1, not n; 1800 starts at n=2
n[(a + f)/2] = 135245210
n[((221400 + 221400+1800(n-1))/2 = 135245210
Solve for n: you'll get n = 284.0448.... ;
You can solve for Sum using n = 284 to get 135,212,400; a bit lesser than the 135,245,210.
As a general case:
s = sum
a = 1st term
b = constant increase
n = number of terms
n = [b - 2a + SQRT(4a^2 - 4ab + b^2 + 8bs)] / [2b]