How to do this?

[Suyash]

Alice's take home pay last year was the same each month,and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her
monthly take -home pay that she did not save.If all the money that she saved last year was from her take-home pay,what
fraction of her take-home pay did she save each month?

a 1/2 b 1/3 c1/4 d 1/5 e 1/6.

i spend a lot of time on this question and got confused in the wording which took me a lot of time during the exam.
The Oa is d.1/5.How to approach it?

[Guest]

Let x be Alice's take home pay
Let y be the portion that Alice saves each month

Algebraic equation for the portion that Alice saves each month for the end of last year:

12xy=3(x-xy)
4xy = x-xy (divide both side 3)
4xy+xy=x
5xy=x (add xy to both side)
5y=1 (divide both side by x)
y = x/5xy (solve for y as requested from the question)
y = 1/5

Please let me know if this helps!

[Guest]

Take out the second to last part of the step...i made an error

[RonPurewal]

Alice's take home pay last year was the same each month,and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her
monthly take -home pay that she did not save.If all the money that she saved last year was from her take-home pay,what
fraction of her take-home pay did she save each month?

a 1/2 b 1/3 c1/4 d 1/5 e 1/6.

i spend a lot of time on this question and got confused in the wording which took me a lot of time during the exam.
The Oa is d.1/5.How to approach it?

in this problem there's no need to use a variable to stand for the take-home pay itself, since the value of the take-home pay is of no interest to us: everything in the problem is stated in terms of fractions of the take-home pay.

if you prefer, or if you're uncomfortable with the prospect of ignoring the dollar amount entirely, you can think of the monthly take-home pay as equal to 1, which will yield the same results.

here's how it works:
she saves y (which is a fraction) each month.
at the end of the year, she's saved 12y.
the problem states that this equals 3 times (1 - y).
12y = 3(1 - y)
12y = 3 - 3y
15y = 3
y = 1/5

there you go.

[Guest]

COOL..BECAME SIMPLER......THANKS