Question

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?

Answer 1

Alice saved 20% of her take home pay each month (0.2)

Explanation:

Allocate variables to each amount :

`x = takehome pay\\y =savings each month\\z =spending each month`

Find the relationships between the variables:

Her spending money is equal to her takehome pay after subtraction her savings:

`z=x-y` .....A

The amount that she had saved by the end of the year is equal to 3 times the amount that she was spending per month. The saved amount by the end of the year should be equal to 12 times her takehome pay minus 12 times her spending.

`12x -12z =3z`

Solve the equations:

`12x-12z=3z\\12x=15z\\x=(15)/(12) z\\`

Now insert equation A into this equation:

`x=(15)/(12) (x-y)\\x=(15)/(12) (x)-(15)/(12) (y)\\(12)/(12) x-(15)/(12) (x)=-(15)/(12) (y)\\-(1)/(4)x= -(15)/(12) (y)\\0.2x=y`