Question

A piece of yellow yarn was 230 inches long. After 90 inches had been cut from it, the piece of yellow yanwas twice as long as a piece of blue yarn. At first, how much longer was the yellow yarn than the blueyard?

Answer 1

Let be "y" the original length of the yellow yarn (in inches)and "b" the length of the blue yarn (in inches).

Knowing that the length of the yellow yarn was 230 inches long and then its length was twice as long as a piece of blue yarn after 90 inches had been cut from it, you can set up the following System of Equations:

`\begin{cases}y=230 \\ y-90=2b\end{cases}`

Now, to find the value of "b", you need to substitute the value of "y" into the second equation and solve for "b" (remember that this is the length of the yarn). Then, you get:

`\begin{gathered} y-90=2b \\ (230)-90=2b \\ 140=2b \\ \\ (140)/(2)=b \\ \\ b=70 \end{gathered}`

Therefore, to calculate how much longer the yellow yarn was than the blue yarn, you need to subtract the value of "b" from "y";

`y-b=230-70=160`

Hence, the answer is: The yellow yarn was 160 inches longer than the blue yarn.