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
