Nutritional information about a breakfast cereal is printed on the box. For instance, one serving of Frosted Flakes has 111 calories, 140 milligrams of sodium, and 1.2 grams of protein. We may represent this as a vector

\begin{equation*} \left[\begin{array}{r} 111 \\ 140 \\ 1.2 \\ \end{array}\right] \text{.} \end{equation*}

One serving of Cocoa Puffs has 120 calories, 105 milligrams of sodium, and 1.0 grams of protein.

  1. Write the vector describing the nutritional content of Cocoa Puffs.

  2. Suppose you eat \(a\) servings of Frosted Flakes and \(b\) servings of Cocoa Puffs. Use the language of vectors and linear combinations to express the total amount of calories, sodium, and protein you have consumed.

  3. How many servings of each cereal have you eaten if you have consumed 342 calories, 385 milligrams of sodium, and 3.4 grams of protein.

  4. Suppose your sister consumed 250 calories, 200 milligrams of sodium, and 4 grams of protein. What can you conclude about her breakfast?