2 cups of low fat yogurt and 3 bannas contain a total of 650 calories .4 cups of low fat yogurt and 2 bannas contain a total of 900 coleries how many calories does a cup of low fat yogurt contain ?

Let x be the number of calories in a cup of low fat yogurt and y be the number of calories in a banana.

From the given information:

2x + 3y = 650 ----(1)
4x + 2y = 900 ----(2)

Now, solve the system of equations (1) and (2) to find the values of x and y.

From equation (1):

2x + 3y = 650
=> 2x = 650 - 3y
=> x = (650 - 3y)/2 ----(3)

From equation (2):

4x + 2y = 900
=> 4(650-3y)/2 + 2y = 900
=> 1300 - 6y + 2y = 900
=> -4y = -400
=> y = 100

Now substitute the value of y back into equation (1):

2x + 3y = 650
2x + 3(100) = 650
2x + 300 = 650
2x = 350
x = 175

Therefore, a cup of low fat yogurt contains 175 calories.