Question

a restaurant makes two kinds of bread: plain bread and cheesy bread. an order of plain bread requires 2 pounds of dough. an order of cheesy bread requires 3 pounds of dough and 1 pound of cheese. the restaurant has 80 pounds of dough and 20 pounds of cheese available each day.
which system of inequalities represents the number of orders of plain bread, x, and cheesy bread, y, that can be made each day?
\\(\boldsymbol{\

$$\begin{cases}2x + 3y \\leq 80 \\\\ x \\leq 20\\end{cases}$$

}\\) (a)
\\(\boldsymbol{\

$$\begin{cases}2x + 3y \\leq 80 \\\\ y \\leq 20\\end{cases}$$

}\\) (b)
\\(\boldsymbol{\

$$\begin{cases}3x + 2y \\leq 80 \\\\ x \\leq 20\\end{cases}$$

}\\) (c)
\\(\boldsymbol{\

$$\begin{cases}3x + 2y \\leq 80 \\\\ y \\leq 20\\end{cases}$$

}\\) (d)

Explanation:

Step1: Analyze dough constraint

Plain bread (x) needs 2 pounds dough, cheesy (y) needs 3 pounds. Total dough ≤ 80: \(2x + 3y \leq 80\).

Step2: Analyze cheese constraint

Only cheesy bread (y) uses cheese, 1 pound per y. Total cheese ≤ 20: \(y \leq 20\).

Step3: Match with options

Check options: Option b has \(2x + 3y \leq 80\) (dough) and \(y \leq 20\) (cheese), which matches.

Answer:

B. \(

$$\begin{cases} 2x + 3y \leq 80 \\ y \leq 20 \end{cases}$$

\)