Please help me to work this out using the inversion method (I'd appreciate if you could provide a step by step breakdown (I don't understand how to do it and my math really sucks!!):

Question

Jim spent 1/3 of his salary on food. He spent 1/4 of it on shoes. He has $400 remaining. What was his original salary?

Just to show that I've tried, here's what I did so far:

1/3 + 1/4


4 + 3
__________ =7/12
12

12/12 - 7/12 = 5/12 (representing $400)

I'm stuck from here. I tried finding the dollar value of 7/12 by finding 1/12 and then multiplying that amount by 7 so I could add it to the 5/12 ($400) but I'm not numbers savvy enough to figure out 1/12 and don't understand how to invert the equation. Don't wanna loose my mind and failure is not an option. Help me please and thank you in advance!!!!!!!

Answer 1

(1/3)s + (1/4)s + 400 = s

400 = 7/12s

400 / (7/12) = s

400 * (12/7) = s

4,800/7 = s

685.71 = salary

Answer 2

1/3 + 1/4 = 4/12 + 3/12 = 7/12 right

12/12 - 7/12 = 5/12 right he has 5/12 left

so 5/12 of salary = 400
multiply both sides by 12/5, the inverse

60/60 of salary = (12/5) * 400

= 12 * 80 = 960

Answer 3

I goofed!