2cups of low fat yogurt and and 3 bananas contain 650 calories, 4 cups of low-fat yogurt and 2 bananas contain 900 calories. how many calories are in the cup of yogurt

A cup of yogurt has 175 calories.

Step-by-step explanation:

We can solve for the amount of calories in one cup of yogurt and in one banana by setting up and solving a system of equations.  Given the information in the problem '2 cups of yogurt and 3 bananas is 650 calories' and '4 cups of yogurt and 2 bananas is 900 calories' we can set up two equations:

2y + 3b = 650 and 4y + 2b = 900, where 'y' is the cups of yogurt and 'b' is the number of bananas.  

Using elimination, we can multiply the first equation by a factor of '-2' and then add the equations together to solve for the remaining variable:

-2(2y + 3b = 650) = -4y - 6b = -1300

-4y - 6b = -1300

+ 4y + 2b = 900

-4b = -400, or b = 100, so each banana has 100 calories, if each banana has 100 calories: 4y + 2(100) = 900 or 4y = 700 or y = 175.  So, each cup of yogurt has 175 calories.

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