Dakota mixes two cereals for breakfast. one gram of cereal a has 6 milligrams of sodium and 7 calories. one gram of cereal b has 8 milligrams of sodium and 5 calories. she wants the bowl of cereal to contain no more than 200 milligrams of sodium and 150 calories. let "a" equal the number of grams of cereal a and "b" equal the number of grams in cereal b, where are "a" > 0 and "b" > 0. which system of inequalities represents the possible ways dakota can mix the cereals.

Number of grams of cereal A = a

Number of grams of cereal B = b

One gram of Cereal A has: 6 mg of sodium and 7 calories

One gram of Cereal A has: 8 mg of sodium and 5 calories

We need to make sure that the cereal contains maximum 200 mg sodium

⇒ Number of grams of cereal A × Sodium quantity in a gram of cereal A + Number of grams of cereal B × Sodium quantity in a gram of cereal B <= 200 mg

Substituting the required values

⇒ a×6 + b×8 <=200

Further simplifying the above equation

⇒ a×3 + b×4 <=100

Further, we need to make sure that the cereal contains maximum 150 calories

⇒ Number of grams of cereal A × Calories in a gram of cereal A + Number of grams of cereal B × Calories in a gram of cereal B <= 150

⇒ a×7 + b×5 <=150

Hence, the system of inequalities that represents the possible mix is:

a×3 + b×4 <=100 AND a×7 + b×5 <=150

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