Many years ago a friend of mine solved a product package problem for me. Now I am struggling to recreate the notation. The problem was there were product bundles including plane, hotel and car rental from alternative providers. Let say Airlines1 is a, Hotel1 is b, Rental1 is c, Airlines2 is d, Hotel2 is e and Rental2 is f. I was informed with only package prices such as:
```
    a+e+c=400
    d+b+f=380
    a+b+d=330
    d+e+c=450
```
My friend defined a matrix in wolframalpha.com and wolframalpha came up with a result such as *"There is one possible solution, a=200, b=100, c=50, d=250, e=150, f=30"*

Now I am trying to replicate the solution again but I am unsuccessful with the syntax. What I've tried so far:
```
    {{a,e,c},{b,d,f},{a,b,d},{d,e,c}}={400,380,330,450}
```
and
```
    LinearSolve[{{a,e,c},{b,d,f},{a,b,d},{d,e,c}},{400,380,330,450}]
```
Could anyone help me please with the correct syntax for the desired solution?