Optimal Consumption (Utility Maximization)?

In the country where I live, there is just 1 sushi shop. This sushi shop only sells two types of sushi: Salmon (S) and Tuna (T). I enjoy both Salmon and Tuna sushi equally as much, and would like some of each every meal.

My utility function can thus be represented by U(S,T) = S^(a)*T^(b), where a+b = 1.

A piece of salmon sushi costs 5 dollars, while a tuna sushi costs 4 dollars. I have 120 dollars to spend on the meal. If I wanted to maximize my utility, how many pieces of salmon and tuna sushi should I eat/buy?

[First to answer correctly gets best answer]

Answer:
answer is T/S= 5b / (4a), or you split your money between T & S in same proportion as b & a. you get that answer from taking derivatives of U w.r.t to S and T, then taking their ratio and setting it equal to ratio of prices.

can't tell exact T & S without knowing a and b

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