Question

A store is having a sale on chocolate chips and walnuts. For 3 pounds of chocolate chips and 5 pounds of walnuts, the total cost is $ 15 . For 12 pounds of chocolate chips and 2 pounds of walnuts, the total cost is $ 33 . Find the cost for each pound of chocolate chips and each pound of walnuts.

Answer 1

c = cost per pound of chocolate chips

w = cost per pound of walnuts.

`\bf \stackrel{\textit{3 lbs of`

`\bf -18w=-27\implies w=\cfrac{-27}{-18}\implies \blacktriangleright w=\cfrac{3}{2} \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{3c+5\left(\cfrac{3}{2} \right)=15}\implies 3c+\cfrac{15}{2}=15 \implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( 3c+\cfrac{15}{2} \right)=2(15)} \\\\\\ 6c+15=30\implies 6c=15\implies c=\cfrac{15}{6}\implies \blacktriangleright c=\cfrac{5}{2} \blacktriangleleft`