Question

The cost of 3 boxes of envelopes and 4 boxes of notebook paper is $13.25. Two boxes of envelopes and 6 boxes of notebook paper cost $17. Find the cost of each.

Answer 1

E = cost of a box of envelopes

N = cost of a box of notebook paper

`\bf \begin{cases} 3E+4N=13.25\\ 4N=13.25-3E\\[0.8em] \boxed{N}=\cfrac{13.25-3E}{4}\\[-0.5em] \hrulefill\\ 2E+6N=17 \end{cases}~\hspace{5em}\stackrel{\textit{substituting \boxed{N} in the 2nd equation}}{2E+6\left( \boxed{\cfrac{13.25-3E}{4}} \right)=17}`

`\bf 2E+\cfrac{79.5-18E}{4}=17\implies\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{8E+79.5-18E=68} \\\\\\ -10E=-11.5\implies E=\cfrac{-11.5}{-10}\implies \blacktriangleright E=1.15 \blacktriangleleft \\\\\\ \stackrel{\textit{and if we substitute that E in the 1st equation}}{3(1.15)+4N=13.25}\implies 3.45+4N=13.25 \\\\\\ 4N=9.8\implies N=\cfrac{9.8}{4}\implies \blacktriangleright N=2.45 \blacktriangleleft`