Question

brad makes his own snack mix using whole grain cereal and mixed nuts. one batch of his recipe makes 6 cups of snack mix. brad uses 3 times as much cereal as mixed nuts. the system below can be used to find the number of cups of cereal and number of cups of mixed nuts brad uses to make one batch of snack mix.
\\(\

$$\begin{cases} c + m = 6 \\\\ \\ \\ \\ \\ \\ \\ \\ m = \\frac{c}{3} \\end{cases}$$

\\)
which describes the ingredients brad uses to make one batch of snack mix?
\\(\circ\\) 2 cups of cereal and 4 cups of mixed nuts
\\(\circ\\) 3 cups of cereal and 9 cups of mixed nuts
\\(\circ\\) 4.5 cups of cereal and 1.5 cups of mixed nuts
\\(\circ\\) 7.5 cups of cereal and 4.5 cups of mixed nuts

Explanation:

Step1: Substitute m into first equation

Substitute $m = \frac{c}{3}$ into $c + m = 6$:
$c + \frac{c}{3} = 6$

Step2: Combine like terms

Combine the terms with $c$:
$\frac{3c}{3} + \frac{c}{3} = 6$
$\frac{4c}{3} = 6$

Step3: Solve for c

Multiply both sides by $\frac{3}{4}$:
$c = 6 \times \frac{3}{4} = 4.5$

Step4: Solve for m

Substitute $c=4.5$ into $m = \frac{c}{3}$:
$m = \frac{4.5}{3} = 1.5$

Answer:

4.5 cups of cereal and 1.5 cups of mixed nuts