Question

I can't figure this out :( Help!!!rac%7B1%7D%7B4%7D%20w%20%2B%2010" id="TexFormula1" title="3 \frac{1}{2} w + 8 = 3 \frac{1}{4} w + 10" alt="3 \frac{1}{2} w + 8 = 3 \frac{1}{4} w + 10" align="absmiddle" class="latex-formula">

Answer 1

let's first off, convert the mixed fractions to improper fractions, and then, let's multiply both sides by the LCD, notice, the LCD will be hmmmm 4, so we'll multiply both sides by 4, to do away with the denominators.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{7}{2}w+8=\cfrac{13}{4}w+10\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4\left( \cfrac{7}{2}w+8 \right)=4\left( \cfrac{13}{4}w+10 \right)} \\\\\\ 14w+32=13w+40\implies w=40-32\implies \boxed{w=8}$