Question

Can you help me with this question? Screenshot Thank you

Answer 1

well, the total amount of rope is really "x".

Now, we know he used 1/4 of that first, if we take 1/4 of a whole or 4/4, that leaves us with 3/4, then he used 5/9 of that for his daughter's rope and he was left with 120 cm.

`\stackrel{ \textit{for the boxes} }{\cfrac{1}{4}x}~~ + ~~\stackrel{ \textit{for skipping rope} }{\stackrel{ remainder }{\left( \cfrac{3}{4}x \right)}\left( \cfrac{5}{9} \right)}~~ + ~~120~~ = ~~\stackrel{ \textit{full length} }{x}`

`\cfrac{x}{4}+\cfrac{3x}{4}\cdot \cfrac{5}{9}+120=x\implies \cfrac{x}{4}+\cfrac{3x}{9}\cdot \cfrac{5}{4}+120=x\implies \cfrac{x}{4}+\cfrac{x}{3}\cdot \cfrac{5}{4}+120=x \\\\\\ \cfrac{x}{4}+\cfrac{5x}{12}+120=x\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{x}{4}+\cfrac{5x}{12}+120 \right)=12(x)} \\\\\\ 3x+5x+1440=12x\implies 8x+1440=12x\implies 1440=4x \\\\\\ \cfrac{1440}{4}=x\implies \boxed{360=x}`