Question

otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. what is the equation that can be used to find the value of y, the total amount of flour that otto used in the recipe, and what are the constraints on the values of x and y?\
\\(\circ\\) \\(y = 5.5x\\), \\(x\\) is any integer greater than or equal to 0, and \\(y\\) is an integer greater than or equal to 5.\
\\(\circ\\) \\(y = 5.5x\\), \\(x\\) is any real number greater than or equal to 0, and \\(y\\) is any real number greater than or equal to 5.5.\
\\(\circ\\) \\(y = x + 5.5\\), \\(x\\) is any integer greater than or equal to 0, and \\(y\\) is an integer greater than or equal to 5.\
\\(\circ\\) \\(y = x + 5.5\\), \\(x\\) is any real number greater than or equal to 0, and \\(y\\) is any real number greater than or equal to 5.5.

Explanation:

Step1: Determine the total flour

Otto used 5.5 cups of whole wheat flour and \( x \) cups of white flour. So the total flour \( y \) is the sum of these two, so the equation is \( y = x + 5.5 \).

Step2: Analyze the domain of \( x \)

The number of cups of flour (either whole wheat or white) can't be negative, so \( x \) must be greater than or equal to 0. Also, the number of cups can be a real number (since you can have a fraction of a cup, like 0.5 cups), so \( x \) is any real number greater than or equal to 0.

Step3: Analyze the range of \( y \)

Since \( y=x + 5.5 \) and \( x\geq0 \), when \( x = 0 \), \( y=5.5 \), and as \( x \) increases, \( y \) increases. Also, \( y \) can be any real number (because \( x \) is a real number) greater than or equal to 5.5 (since \( x\geq0\) implies \( y=x + 5.5\geq5.5\)).

Answer:

\( y=x + 5.5 \); \( x \) is any real number greater than or equal to 0, and \( y \) is any real number greater than or equal to 5.5 (corresponding to the last option: \( y=x + 5.5 \); \( x \) is any real number greater than or equal to 0, and \( y \) is any real number greater than or equal to 5.5)