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 = 12
fM
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: 12
fM = 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
