Problem Solving

Alice’s take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home 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.

oa [spoiler]1/5[/spoiler]

For me it worked best to pick numbers b/c you are getting your answer in fraction form anyway.

Monthly pay = 100

portion saved monthly = x

so for the year she saved 12*x
which equals 3*(amount she did not save) = 3*(100-x)

so 12x = 3*(100-x)

4x = 100 - x

5x = 100

x = 20

so the fraction she saved every month would be 20/100 = 1/5

ssmiles08, good job. i was trying w/out picking numbers and it didn't work out..... let's see if someone else can give the answer only using variables...

Let x be her monthly take home pay

Yearly = 12x

let y be the amount she save at the end of the year

therefore, y= 3*(x - y/12)

y = 3x/12 - 3y/12

y= x/4 - y/4 = (x-y)/4

4y = x - y

5y = x

y = x/5

fraction of her take home pay she saved each month = x/5 / x = x/5x = 1/5

Hope this helps.

salary per month = 100
Savings = s
Expenses = 3

12s = 3e

s = 1/4 e

therefore 1/4 e + e = 100

e = 80
s = 1/4 e = 20

Fraction of saving = 20/100 = 1/5