SOLUTION: Lauren has $1,200.00. She plans to take $10.00 out of her account, the 1st week, after that she adds $10 to the amount each week. example is 1st week is $10.00, 2nd week is $20.00

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Question 188531: Lauren has $1,200.00. She plans to take $10.00 out of her account, the 1st week, after that she adds $10 to the amount each week. example is 1st week is $10.00, 2nd week is $20.00, 3 week is $30.00 and so on. How many weeks before her account is empty?
My teacher said to use the following formula:
1200 = $10 + (n-1)$10
But when I figure it out it comes up with 120 and I know that is incorrect.
Do you know what part of the formula that I am missing or is there another formula I should be using?
thank you for any help you can give me.
Lauren Pease

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The formula you have is just a complicated way of computing the amount taken any given week. Note that:

What you need is a formula for the sum of all the weeks withdrawals in terms of n which can be set equal to 1200

Which is just a shorthand way of saying:

Fortunately, there is a simple formula for computing such a sum; add the first number to the last number, multiply the sum by the number of numbers, and then divide that product by 2: (if you write back and ask, I'll explain why this works)

And this all has to be equal to 1200 so:

Simplify:

Factor the quadratic:

So

or

We can exclude -16 for this problem because emptying the account 16 weeks before she started to withdraw is absurd. This is an extraneous root introduced by the act of squaring the variable in the process of solving the problem. The positive root, 15, is the number of the week when she will withdraw the last $150 from her account.

John