Each ounce of a substance A supplies 2% of the nutrition a patient needs. Substance B supplies 15% of the required nutrition per ounce, and substance C supplies 15% of the required nutrition per ounce. If digestive restrictions require that substances A and C be given in equal amounts, and the amount of substance B be one-fifth of either of these other amounts, find the number of ounces of each substance that should be in the meal to provide 100% of the required nutrition.
To solve this problem, we can start by assigning variables to the unknowns. Let's say:
Let x be the number of ounces of substance A and C.
Let y be the number of ounces of substance B.
According to the problem statement, substance A supplies 2% of the required nutrition per ounce, substance B supplies 15%, and substance C supplies 15%.
So, for each ounce of substance A, it contributes 2% of the required nutrition. Therefore, x ounces of substance A would contribute 2x% of the required nutrition.
Similarly, x ounces of substance C would contribute 15x% of the required nutrition.
Given that the digestive restrictions require substances A and C to be given in equal amounts, we know that x ounces of substance A would be equal to x ounces of substance C.
Now, the amount of substance B (y ounces) is one-fifth of either of these other amounts. So, we have:
y = (1/5)x
To find the total amount of nutrition provided, we need to sum up the contributions from each substance. It should add up to 100% of the required nutrition.
The sum of the contributions from substances A, B, and C is:
2x% + 15% + 15x% = 100%
Now, let's solve for x:
2x + 15 + 15x = 100
17x + 15 = 100
17x = 85
x = 5
Now we can substitute the value of x in the equation y = (1/5)x:
y = (1/5) * 5
y = 1
Therefore, the number of ounces of substance A and C should be 5 ounces each, and the number of ounces of substance B should be 1 ounce to provide 100% of the required nutrition.