Question

A candy maker mixed marshmallows worth $1.80 a pound with rice crisipes worth $3.20 a pound to make 50 pounds of a rice crispie treats worth $2.92 a pound. Find the number of pounds of each item used.

Answer 1

`\bf \begin{array}{lccclll} &amount&price&\textit{price per amount}\\ &-----&-----&--------\\ \textit{marshmallows}&x&1.80&(1.80)(x)\\ \textit{rice crispies}&y&3.20&(3.20)(y)\\ -----&-----&-----&--------\\ mixture&50&2.92&(50)(2.92) \end{array}\\\\ -----------------------------\\\\ \begin{cases} x+y=50\implies \boxed{y}=50-x\\ 1.80x+3.20y=(50)(2.92)\\ ----------\\ 1.80x+3.20\left( \boxed{50-x} \right)=(50)(2.92) \end{cases}`

solve for "x", to see how many lbs of marshmallows were needed

what about "y"? well, y = 50 - x