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!!):

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!!!!!!!

(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

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

I goofed!

No worries, I'll guide you through the process step by step. Let's start from where you left off.

You correctly found that Jim has 5/12 of his original salary remaining, which represents $400. Now, to find his original salary, we need to find the value of 1/12 of his salary. We can do this by inverting the fraction using the fact that 1 divided by a fraction is equal to the fraction flipped:

1/(5/12)

To simplify this division, we multiply the numerator by the reciprocal (or flip) the denominator:

1 * (12/5) = 12/5

So, 1/12 of Jim's salary is equal to 12/5.

Now, to find the whole salary, we multiply both sides of the equation by 12.

12/5 * 12 = 144/5

Therefore, Jim's original salary is 144/5 or $28.80.