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.