To solve this problem, let's assume the number of calories per cup of sunflower seeds is represented as "x". Since the number of calories per cup of raisins is 400 less than the number of calories per cup of sunflower seeds, we can represent the number of calories per cup of raisins as "x - 400".
Now, let's use this information to set up an equation based on the total number of calories in the mixture.
Paula mixed 2 cups of sunflower seeds and 3 cups of raisins, so the total number of calories in the mixture can be calculated as follows:
2 cups of sunflower seeds * x calories per cup + 3 cups of raisins * (x - 400) calories per cup = 2900 calories
Simplifying the equation, we have:
2x + 3(x - 400) = 2900
Now, expand and solve the equation:
2x + 3x - 1200 = 2900
5x - 1200 = 2900
Add 1200 to both sides of the equation to isolate the variable:
5x = 4100
Divide both sides of the equation by 5 to solve for x:
x = 820
So, the number of calories per cup of sunflower seeds is 820.
To find the number of calories per cup of raisins, substitute this value back into the equation for "x - 400":
820 - 400 = 420
Therefore, the number of calories per cup of raisins is 420.