Respuesta :
Given:
The length of yarn needed, l=23 1/4 feet.
The length of a yarn bundle, L=11 1/2 feet.
The number of bundles of yarn needed can be calculated as,
[tex]\begin{gathered} n=\frac{l}{L}=\frac{23\text{ }\frac{1}{4}}{11\frac{1}{2}} \\ n=\frac{\frac{23\times4+1}{4}}{\frac{11\times2+1}{2}} \\ n=\frac{\frac{93}{4}}{\frac{23}{2}} \\ n=\frac{93}{4}\times\frac{2}{23} \\ n=\frac{93}{2}\times\frac{1}{23} \\ n=\frac{93}{46} \\ n=2\frac{1}{46} \end{gathered}[/tex]Therefore, 3 bundles is needed by Jenna to make the scarf.
The part of leftover yarn is,
[tex]\begin{gathered} N^{}=3-2\frac{1}{46} \\ =3-(2+\frac{1}{46}) \\ =1-\frac{1}{46} \\ =\frac{46-1}{46} \\ =\frac{45}{46} \end{gathered}[/tex]Hence, 45/46 part of a bundle of yarn will be left.
Now, the length of leftover yarn is,
[tex]\begin{gathered} l^{\prime}=N\times L \\ =\frac{45}{46}\times11\frac{1}{2} \\ =\frac{45}{46}\times\frac{11\times2+1}{2} \\ =\frac{45}{46}\times\frac{23}{2} \\ =\frac{45}{2}\times\frac{1}{2} \\ =\frac{45}{4} \\ =11\frac{1}{4}\text{feet} \end{gathered}[/tex]Therefore, 111/4 feet of yarn will be left.
