Paula mixed 2 cups of sunflower seeds and 3 cups of raisins yo make a snack for a hike. She figured that the mixture would provide her with 2900 calories of food energy. Finf the number of calories per cup of raisins if it is 400 less than the number of calories per cup of sunflower seeds. I came up with 820 per cup sunflower and 420 per cup raisins but how would I write the equation?

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.

To write the equation, we can assign variables to the unknown values. Let's call the number of calories per cup of sunflower seeds as "x", and the number of calories per cup of raisins as "y".

From the given information, we know that Paula mixed 2 cups of sunflower seeds and 3 cups of raisins, and the total calories of the mixture is 2900.

The equation can be written as:
(2 * x) + (3 * y) = 2900

Now, it is also given that the number of calories per cup of raisins is 400 less than the number of calories per cup of sunflower seeds. Mathematically, we can express this relationship as:
y = x - 400

These two equations can be used to solve for the values of x and y.