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 𝑥 to represent the mass of the
first type of baby food in grams and 𝑦 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 𝑥 represent the mass
of the first type of baby food and 𝑦 represent the mass of the second type. Since these are masses given in
grams, we know that both 𝑥 and 𝑦 must be nonnegative. Therefore, 𝑥 is greater than or
equal to zero, and 𝑦 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 we’re also told that a baby
needs at least 100 units of vitamin A per day, we know that two 𝑥 plus three 𝑦
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 𝑥 plus two 𝑦 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. 𝑥 is greater than or equal to
zero, 𝑦 is greater than or equal to zero, two 𝑥 plus three 𝑦 is greater than or
equal to 100, and three 𝑥 plus two 𝑦 is greater than or equal to 120.
