Kallie Fritz

2022-09-24

A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $8.60 per pound should be mixed with trail mix costing $3.00 per pound to create a 27 pound mixture worth $5.90 per pound.

Phoenix Morse

Beginner2022-09-25Added 10 answers

let nequired chocolate x pounds

now, $$x+y=27$$

And $$8.6x+3y=5.9(x+y)\phantom{\rule{0ex}{0ex}}\Rightarrow 8.6x+3(27-x)=5.9(x+27-x)\phantom{\rule{0ex}{0ex}}\Rightarrow 8.6x-3x+81=159.3\phantom{\rule{0ex}{0ex}}\Rightarrow 5.6x=159.3-81\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{78.3}{5.6}\phantom{\rule{0ex}{0ex}}\Rightarrow x=13.98\phantom{\rule{0ex}{0ex}}\Rightarrow x=14\phantom{\rule{0ex}{0ex}}\Rightarrow y=13$$

so needs 14 pounds chocolate

13 pounds trail

now, $$x+y=27$$

And $$8.6x+3y=5.9(x+y)\phantom{\rule{0ex}{0ex}}\Rightarrow 8.6x+3(27-x)=5.9(x+27-x)\phantom{\rule{0ex}{0ex}}\Rightarrow 8.6x-3x+81=159.3\phantom{\rule{0ex}{0ex}}\Rightarrow 5.6x=159.3-81\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{78.3}{5.6}\phantom{\rule{0ex}{0ex}}\Rightarrow x=13.98\phantom{\rule{0ex}{0ex}}\Rightarrow x=14\phantom{\rule{0ex}{0ex}}\Rightarrow y=13$$

so needs 14 pounds chocolate

13 pounds trail

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