Question

Each ounce of a substance A supplies 3% of the nutrition a patient needs. Substance B supplies 10% 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 be1 1/5

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.
Incorrect: Your answer is incorrect.
______oz of substance A
______oz of substance B
______oz of substance C

Answer 1

To achieve 100% nutrition, we need 3.33 ounces each of substance A and C, and 4 ounces of substance B, based on their respective nutrition percentages and the given ratios.

Step-by-step explanation:

Let the number of ounces of substances A and C be x, since the digestive restrictions require that these substances are given in equal amounts. The amount of substance B must be 1 1/5 times x, which can be expressed as 1.2x. To provide 100% of the required nutrition, the sum of the nutrition provided by these substances must equal 100%, which can be set up as an equation:

3% × x (Substance A) + 10% × 1.2x (Substance B) + 15% × x (Substance C) = 100%

Solving for x gives the following steps:

(0.03 + 0.12 + 0.15)x = 1

0.30x = 1

x = 1 / 0.30

x = 3.33 ounces

Therefore:

Substance A = 3.33 oz

Substance B = 1.2 × 3.33 = 4 oz

Substance C = 3.33 oz

Answer 2

x = 17.2 oz of substance A and C

x = 3.7 oz of substance B

Step-by-step explanation:

This is a word problem in mathematical optimization, which involves finding the values that maximize or minimize some objective function. To solve this problem, we need to find the optimal number of ounces of each substance to provide 100% of the required nutrition.

Let x be the number of ounces of substance A and C. Then the amount of substance B is 1 1/5 times either of these, or 1 1/5 x.

Since each ounce of substance A supplies 3% of the nutrition, the total contribution from A is 3x%. Similarly, the total contribution from B is 10 * 1 1/5 x = 11 x/5% and from C is 15x%.

The objective is to find x such that the total contribution from all three substances is 100%, or 3x + 11 x/5 + 15x = 100.

Solving for x, we have

29x/5 = 100

x = 100 * 5 / 29 = 17.24 oz

So, 17.24 oz of substance A and C, and 1 1/5 * 17.24 oz = 3.65 oz of substance B should be in the meal. Rounding to the nearest tenth, we have:

x = 17.2 oz of substance A and C

x = 3.7 oz of substance B