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.

Let x be the number of ounces of substance A in the meal. Then, the number of ounces of substance C also equals x, and the number of ounces of substance B equals x/5 (one-fifth of x).

We can express the total nutrition provided by each substance in terms of x:
- Substance A provides 2% * x or 0.02x
- Substance B provides 15% * (x/5) or 0.15x
- Substance C provides 15% * x or 0.15x

To provide 100% of the required nutrition, we need the following equation to hold:

0.02x + 0.15(x/5) + 0.15x = 1

Solving for x:
0.02x + 0.03x + 0.15x = 1
0.20x = 1
x = 5

Thus, there should be 5 ounces of substance A, 5 ounces of substance C, and 5/5=1 ounce of substance B in the meal to provide 100% of the required nutrition.

To solve this problem, we'll set up a system of equations based on the given information:

Let x be the number of ounces of substance A and substance C each.
Let y be the number of ounces of substance B.

1) Each ounce of substance A supplies 2% of the required nutrition:
Substance A provides 0.02 * x ounces of nutrition.

2) Substance B supplies 15% of the required nutrition per ounce:
Substance B provides 0.15 * y ounces of nutrition.

3) Substance C supplies 15% of the required nutrition per ounce:
Substance C provides 0.15 * x ounces of nutrition.

4) Substance B should be one-fifth of the amount of substances A or C:
y = (1/5) * x

5) The total nutrition provided by the meal should be 100%:
0.02 * x + 0.15 * y + 0.15 * x = 1

Now, let's solve this system of equations:

First, substitute Equation 4) into equations 2) and 3):

0.15 * (1/5) * x + 0.15 * x = 0.03 * x + 0.15 * x = 0.18 * x

Now, substitute this back into Equation 5):

0.02 * x + 0.18 * x = 1

Combining like terms:

0.2 * x = 1

Divide both sides by 0.2:

x = 5

So, each substance A and substance C should be 5 ounces.

Substituting this into Equation 4), we can find the number of ounces of substance B:

y = (1/5) * 5 = 1

Therefore, one ounce of substance B should be included in the meal.

In conclusion, to provide 100% of the required nutrition, the meal should contain 5 ounces of substance A and C each, and 1 ounce of substance B.

Let's assume that the required nutrition is represented by the variable N.

Given:
- Substance A supplies 2% of the required nutrition per ounce.
- Substance B supplies 15% of the required nutrition per ounce.
- Substance C supplies 15% of the required nutrition per ounce.
- Digestive restrictions require substances A and C to be given in equal amounts.
- Substance B is one-fifth the amount of substances A or C.

Let's start by representing the amount of substance A as x ounces.

Since substance B is one-fifth the amount of substances A or C, the amount of substance B will be (1/5)x ounces.

Since substance C should be given in equal amounts as substance A, the amount of substance C will also be x ounces.

Now, let's calculate the nutrition supplied by each substance.

Substance A supplies 2% of the required nutrition per ounce.
Therefore, the nutrition supplied by substance A will be 0.02Nx (2% of the required nutrition multiplied by the amount x).

Substance B supplies 15% of the required nutrition per ounce.
Therefore, the nutrition supplied by substance B will be 0.15N(1/5)x (15% of the required nutrition multiplied by one-fifth of the amount x).

Substance C supplies 15% of the required nutrition per ounce.
Therefore, the nutrition supplied by substance C will be 0.15Nx (15% of the required nutrition multiplied by the amount x).

To provide 100% of the required nutrition, the nutrition supplied by all substances should be equal to N.

Now, let's write an equation to represent this:

0.02Nx + 0.15N(1/5)x + 0.15Nx = N

Simplifying the equation:

0.02Nx + 0.03Nx + 0.15Nx = N

0.20Nx = N

Dividing both sides by N:

0.20x = 1

x = 1 / 0.20

x = 5 ounces

Since the amount of substance C is equal to the amount of substance A, it will also be 5 ounces.

The amount of substance B is one-fifth of either substance A or C, which means it will be 1 ounce (1/5 of 5 ounces).

So, to provide 100% of the required nutrition, the meal should contain:
- 5 ounces of substance A
- 1 ounce of substance B
- 5 ounces of substance C