Question

A ten foot long board is cut into 3 pieces. The second piece is half as long as the first. The third piece is 4 1/2 feet longer than the second piece. How long is the first piece?

Answer 1

say "a" is the length of the first piece, we'll first off, change the mixed fraction to "improper" and add the pieces, keeping in mind that, all 3 pieces add up to 10 feet.


`\bf \stackrel{mixed}{4(1)/(2)}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}\\\\ -------------------------------`


`\bf \stackrel{\textit{first piece}}{a}+\stackrel{\textit{second piece}}{\cfrac{a}{2}}+\left(\stackrel{\textit{third piece}}{\cfrac{a}{2}~+~\cfrac{9}{2}}\right)=10\impliedby \begin{array}{llll} \textit{multiplying both sides by }\\ \textit{the LCD of 2} \end{array} \\\\\\ 2\left( a+\cfrac{a}{2}+\cfrac{a}{2}+\cfrac{9}{2} \right)=2(10)\implies 2a+a+a+9=20 \\\\\\ 4a=11\implies a=\cfrac{11}{4}\implies a=2(3)/(4)`