Question

Jenna is making a scarf. She needs 23 /4 feet of yarn. Each yarn bundle is 11 1/2feet. How many bundles does Jenna need? How much will be left over?

Answer 1

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,

`\begin{gathered} n=(l)/(L)=\frac{23\text{ }(1)/(4)}{11(1)/(2)} \\ n=((23*4+1)/(4))/((11*2+1)/(2)) \\ n=((93)/(4))/((23)/(2)) \\ n=(93)/(4)*(2)/(23) \\ n=(93)/(2)*(1)/(23) \\ n=(93)/(46) \\ n=2(1)/(46) \end{gathered}`

Therefore, 3 bundles is needed by Jenna to make the scarf.

The part of leftover yarn is,

`\begin{gathered} N^{}=3-2(1)/(46) \\ =3-(2+(1)/(46)) \\ =1-(1)/(46) \\ =(46-1)/(46) \\ =(45)/(46) \end{gathered}`

Hence, 45/46 part of a bundle of yarn will be left.

Now, the length of leftover yarn is,

`\begin{gathered} l^(\prime)=N* L \\ =(45)/(46)*11(1)/(2) \\ =(45)/(46)*(11*2+1)/(2) \\ =(45)/(46)*(23)/(2) \\ =(45)/(2)*(1)/(2) \\ =(45)/(4) \\ =11(1)/(4)\text{feet} \end{gathered}`

Therefore, 111/4 feet of yarn will be left.