SOLUTION: Ida owed her parents x dollars. Last month she paid 1/6 of the amount owed. This month she paid 1/6 of the remaining amoun plus $20.00. In terms of x, how much money does she still

Question 579308: Ida owed her parents x dollars. Last month she paid 1/6 of the amount owed. This month she paid 1/6 of the remaining amoun plus $20.00. In terms of x, how much money does she still owe?
A) (x-2)/(6)
B) (5/6)x - 20
C) (5x-20)/(6)
D) (25/36)x - 20
E) (25x-20)/(36)
I'm confused and I don't know how to approach and solve this..
Thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
she owed her parents x dollars.
last month she paid 1/6 of the amount owed.
she still owes x - (1/6)*x = (5/6)*x of the amount owed.
this month she paid 1/6 of the remaining amount plus $20.00 dollars.
the remaining amount is (5/6)*x
she paid (1/6)*(5/6)*x of it back plus she gave them an additional $20.00.
the amount remaining in the account is therefore equal to:
(5/6)*x - (1/6)*(5/6)*x - $20.00
if you simplify this equation, you will get:
(5/6)*x - (5/36)*x - $20.00
if you multiply (5/6) by (6/6), you will get (30/36).
this means that (5/6) is equivalent to (30/36) and you can substitute for (5/6) in your equation to get:
(5/6)*x - (5/36)*x - $20.00 becomes:
(30/6)*x - (5/36)*x - $20.00
since the denominator is now the same, you can combine the 2 fractions into 1 to get:
((30 - 5)/36)*x - $20.00 which can be simplified to:
(25/36)*x - $20.00

looking at your possible solutions, the one that looks like it will fit is selection D.

let's see how this works.
suppose she owed $36.00
if we use the formula, then she should still owe (25/36)*36 - 20 which would be equal to $5.00

if we calculate it step by step, we would get:
first month she pays 1/6 of 36 dollars which means she pays 6 dollars which means she still owes 30 dollars.
second month she pays 1/6 of 30 dollars which means she pays 5 dollars which means she still owes 25 dollars.
she then pays an additional 20 dollars and she still owes 5 dollars.

the formula and the manual calculations agree so we're good.

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