SOLUTION: Mary spends 1/2 of her income on rent and food, 1/12 on entertainment, and 1/4 of her income on clothing. She saves the rest, which is $500. What is her monthly income? I figure o

Algebra ->  Finance -> SOLUTION: Mary spends 1/2 of her income on rent and food, 1/12 on entertainment, and 1/4 of her income on clothing. She saves the rest, which is $500. What is her monthly income? I figure o      Log On


   

Question 1052183: Mary spends 1/2 of her income on rent and food, 1/12 on entertainment, and 1/4 of her income on clothing. She saves the rest, which is $500. What is her monthly income?
I figure out that LCD is 12 but have not been able to figure out from there.
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Figure out what is left first.
1%2F2%2B1%2F12%2B1%2F4%2BX=1
6%2F12%2B1%2F12%2B3%2F12%2BX=1
10%2F12%2BX=12%2F12
X=2%2F12
X=1%2F6
So she has 1/6 of her income left which is equal to $500.
%281%2F6%29M=500
M=3000
So her monthly income is $3000.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Mary spends 1/2 of her income on rent and food, 1/12 on entertainment, and 1/4 of her income on clothing. She saves the rest, which is $500. What is her monthly income?
I figure out that LCD is 12 but have not been able to figure out from there. 
Let income be I

Then we get: %281%2F2%29I+%2B+%281%2F12%29I+%2B+%281%2F4%29I+%2B+500+=+I

I%2F2+%2B+I%2F12+%2B+I%2F4+%2B+500+=+I

6I + I + 3I + 6,000 = 12I -------- Multiplying by LCD, 12

10I + 6,000 = 12I

6,000 = 12I - 10I

6,000 = 2I

I, or income = %226%2C000%22%2F2, or highlight_green%28%22%243%2C000%22%29