Question

Chubb early on a snack store and is showing Billy Bob how to make some of the items he sells currently he is showing Billy Bob how to correctly mix plain popcorn and caramel popcorn for his best-selling snack Ermac snack mix to make 10 pounds of the snack mix that will sell for $2.50 per pound he adds plain popcorn that cost $3 per pound and caramel popcorn that cost $2.20 per pound how much did he use of each ingredient

Answer 1

$\bf \begin{array}{lccclll} &\stackrel{lb}{amount}&\stackrel{lb}{price}&\stackrel{total}{price}\\ &------&------&------\\ \textit{plain popcorn}&p&3&3p\\ \textit{caramel popcorn}&c&2.2&2.2c\\ -------&------&------&------\\ mixture&10&2.5&25 \end{array}$

so hmm whatever "p" and "c" are, we know that p + c = 10.

and we also know that 3p + 2.2c = 25

thus

$\bf \begin{cases} p+c=10\implies \boxed{c}=10-p\\ 3p+2.2c=25\\ ----------\\ 3p+2.2\left(\boxed{10-p} \right)=25 \end{cases} \\\\\\ 3p+22-2.2p=25\implies 3p-2.2p=25-22\implies 0.8p=3 \\\\\\ p=\cfrac{3}{0.8}\implies p=\cfrac{15}{4}\implies p=3.75$

how much will it be needed for caramel popcorn?  well, c = 10 - p.