Comparable salary in a different city calculations

Question

I am doing a salary comparison depending on 2 cities. Very similar to this website

So you select a source city, then a destination city, your current salary in the source city and it will output the "comparable" salary in the destination city. I want to confirm that what I am doing is correct, just bare with me for a minute. I will give you an example. All the data is fictional.

Source city: Cleveland, OH 
Destination city: Seattle, WA 
Cleveland Salary: $120,000

The way I compare is I take the housing prices, transportation prices and see where it's higher/lower. So, let's assume I will take into consideration only these two pieces of spending: housing and transportation.

On average housing represents 30% of spending, while transportation is 20%. Let's assume that housing is 10% more expensive in Seattle, while transportation is 5% cheaper.

Now, here is where I want your help. Am I doing this right?

1. 30% + 20% = 50% in salary will fluctuate (since I take into consideration only these two spendures)
2. Total amount that will fluctuate from source salary is: $120,000 - 50% = 60K
3. Housing is 30% (=$36,000) from 60K
4. Transportation is 20% (=$24,000) from 60K
5. Housing is 10% higher, so 36K + 10% (3,6K) = $39,600
6. Transportation is 5% lower, so 24K - 5% (1,2K) = $22,800
7. Comparable Salary in Seattle would be (the untouched) 60K + 39,600 + 22,800 = $122,400

Do these calculations seem right to you?

Answer 1

Works out nicely. A somewhat more condensed version of the calculation is

Predicted Seattle Salary = 120000*(1-.3-.2)+120000*(1.1*.3)+120000*(.95*.2) = 122400

Using this in XL might speed up your work.

Answer 2

Or an even more condensed version, which helps really break it down into how the different elements contribute to the result:

120000 * (0.3*1.1 + 0.2* 0.95 + 0.5*1)