Question

I gave my brother 1/5 of my candy, 1/4 to my friend and had 11 pieces left over. How many pieces did I give my brother?

Answer 1

x = total number of candies

`\bf \stackrel{\textit{my brother}}{\cfrac{1}{5}x}+\stackrel{\textit{my friend}}{\cfrac{1}{4}x}+11~~=~~\stackrel{\textit{total}}{x} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{x}{5}+\cfrac{x}{4}+11 \right)=20(x)}\implies 4x+5x+220=20x\implies 9x+220=20x \\\\\\ 220=11x\implies \cfrac{220}{11}=x\implies 20=x~\hspace{10em}\stackrel{\textit{to my brother}}{\cfrac{20}{5}\implies 4}`