Alice's take-home pay

crackgmat007 wrote:Can someone solve this pls?

A fraction of something can mean .5, .4, .9 etc. So let f stand for one of these fractions. A fraction of your paycheck of $3000, say that fraction is half will be .5 x 3000= 1500. To get the other part of the fraction, just take it from one. so 1-.5=.5. With these principles behind you, you are are ready to attack.

If x is how much he makes each month and there are 12 months you know his annual income is

12x

Let f be the fraction in question. If he saved the same fraction each year you know he safed fx each month times 12 is his annual savings:
12fx

Since f is the fraction he saved. 1-f will be the fraction he did not save( if he saved 30% then he consumed 70%) . Putting everything together
Annual savings is 3 times part of income not saved in one month
12fx = 3 (1-f)x
12fx =3x -3fx
15fx=3x
f=3/15
f=1/5

Another way to do this (I'm not that great at math) would be to look to the answer choices.

We know that she's saving a portion of her monthly take home pay each month, and the amount she's saved by the end of the year is three times the amount she doesn't save per month.

So I would plug in a number and pick an answer choice. I'd probably pick $100 since that's an easy number.

Okay, so if we start with answer choice C:

1/4 (100) = 25
25 * 12 months/year = 300

We know if she's saving $25, she's not saving $75. But 75 * 3 != 300, so we know it's not 1/4.

I tend to move down if I'm not sure exactly which way the answer goes. So I'd try answer choice D

1/5 (100) = 20
20 * 12 = 240

Saving $20 means not saving $80

80 * 3 = 240

So answer choice D is correct.

The algebra is usually more difficult for me to solve out than just plugging in numbers/the answer choices.

thanks guys!