Question Video: Determining a Set of Inequalities That Describes a System Expressed in a Word Problem Mathematics

A baby food factory produces two types of baby food. The first type contains 2 units of vitamin A and 3 units of vitamin B per gram. The second type contains 3 units of vitamin A and 2 units of vitamin B per gram. If a baby needs at least 100 units of vitamin A and 120 units of vitamin B per day, state the system of inequalities that describes the food that the baby must eat each day to meet these requirements. Use π₯ to represent the mass of the first type of baby food (in grams) and π¦ to represent the mass of the second type of baby food (in grams).

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Video Transcript

A baby food factory produces two types of baby food. The first type contains two units of vitamin A and three units of vitamin B per gram. The second type contains three units of vitamin A and two units of vitamin B per gram. If a baby needs at least 100 units of vitamin A and 120 units of vitamin B per day, state the system of inequalities that describes the food that the baby must eat each day to meet these requirements. Use π₯ to represent the mass of the first type of baby food in grams and π¦ to represent the mass of the second type of baby food in grams.

In this question, we are told that a factory produces two types of baby food. We will let π₯ represent the mass of the first type of baby food and π¦ represent the mass of the second type. Since these are masses given in grams, we know that both π₯ and π¦ must be nonnegative. Therefore, π₯ is greater than or equal to zero, and π¦ is greater than or equal to zero. We know that the first type of baby food contains two units of vitamin A per gram and the second type contains three units of vitamin A per gram. As weβre also told that a baby needs at least 100 units of vitamin A per day, we know that two π₯ plus three π¦ must be greater than or equal to 100.

We can find a similar inequality for vitamin B. The first type of baby food contains three units, and the second type contains two units. As a baby requires 120 units of vitamin B per day, we have three π₯ plus two π¦ is greater than or equal to 120. We can therefore conclude that we have a system of four inequalities that describes the food that a baby must eat each day. π₯ is greater than or equal to zero, π¦ is greater than or equal to zero, two π₯ plus three π¦ is greater than or equal to 100, and three π₯ plus two π¦ is greater than or equal to 120.