Cheese12 wrote: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
C) 1/4
D) 1/5
E) 1/6

Here's another algebraic approach.

Let M = Alice's monthly take home pay
Let f = the fraction we'll use to calculate monthly savings
The means that fM = the amount of $ Alice saves each month.
And this means that her annual savings = 12fM

Important: If f = the fraction used to calculate monthly savings, then 1-f = the fraction used to calculate amount not saved
The means that (1-f)M = the amount of $ Alice doesn't save each month.

Now we're ready to write an equation.

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.
We get: 12fM = 3(1-f)M
Now solve for f
Expand to get: 12fM = 3M - 3fM
Simplify: 15fM = 3M
Divide both sides by 15M to get: f = 3M/15M =
1/5

Answer: D

Cheers,
Brent

Cheese12 wrote: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
C) 1/4
D) 1/5
E) 1/6


OA: D

We are given 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.

To start, we can let S = the amount of money Alice saved each month and N = the amount of money she did not save each month.
Since 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, we know that:

12S = 3N

4S = N

We need to determine what fraction of her take-home pay she saved each month. Setting this question up as an expression we have:
S/(S + N)= ?

Since 4S = N, we can substitute 4S for N in the expression S/(S + N).

S/(S + 4S) = S/5S = 1/5

Answer: D