Question

Tropical dried fruit costs $1.50 per pound and regular dried fruit costs $0.90 per pound. You want to create a mixed bag of tropical dried fruit and regular dried fruit that is worth $1.30 per pound. How many pounds of tropical dried fruit do you need if you have already purchased 50 pounds of regular dried fruit?

Answer 1

t = total amount of lbs of Tropical dried fruit

m = total amount of lbs of mixed bag

$\begin{array}{lcccl} &\stackrel{fruit}{lbs}&\stackrel{per~lb}{price}&\stackrel{total}{price}\\ \cline{2-4}&\\ \textit{tropical fruit}&t&1.50&1.5t\\ \textit{regular fruit}&50&0.90&45\\ \cline{2-4}&\\ \textit{mix bag}&m&1.30&1.3m \end{array}~\hfill \begin{cases} t+50=m\\ 1.5t+45=1.3m \end{cases} \\\\[-0.35em] ~\dotfill$

$\stackrel{\textit{substituting on the 1st equation}}{1.5t+45=1.3\stackrel{m}{(t+50)}}\implies 1.5t+45=1.3t+65\implies 0.2t+45=65 \\\\\\ 0.2t=20\implies t=\cfrac{20}{0.2}\implies \boxed{t=100}$