Problem Solving

RachelAL wrote:Some of these problems are driving me nuts. I am missing something for sure. Any help would be much appreciated. Thanks!

Alices take home pay 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 saved at the end of the year was 3 times the amount of that portion of her monthly take home pay she did not save. If all the money she saved last year was from take home pay, what fraction of her take home pay did she save each month?

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 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: 1/5

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 money that she saved last year was from her take-home pay, what fraction of her take-home pay did she saved 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
= D

Cheers,
Brent