Solving for y in a Textbook Problem: Understanding the Next Step | Helpful Tips

[powp]

Hello

I am doing this problem in my textbook and I am not sure what is happing in this one step.

2y = 360 \sqrt{\pi} - \sqrt{\pi}y

Trying to solve for y and this is what they show as the next step

(2 + \sqrt{\pi})y = 360 \sqrt{\pi}

Where does this (2 + \sqrt{\pi}) come from?? where did the other y go and the -\sqrt{\pi}?

 

[Nylex]

The (2 + \sqrt{\pi})y came from adding \sqrt{\pi}y to both sides and then factoring out a y from the left hand side. Have you not learned about collecting terms??

2y = 360 \sqrt{\pi} - \sqrt{\pi}y

2y + \sqrt{\pi}y = 360\sqrt{\pi} + \sqrt{\pi}y - \sqrt{\pi}y

(2y + \sqrt{\pi})y = 360\sqrt{\pi}

 

[Jameson]

They added \sqrt{\pi}y to both sides.

Now on the left side of the equation we get 2y + \sqrt{\pi}y

and on the right we get 360\sqrt{\pi}

Now on the left side, they factored out the y so you can solve for it.

2y + \sqrt{\pi}y = y(2 + \sqrt{\pi})

Now putting all of this info together we get

(2 + \sqrt{\pi})y = 360 \sqrt{\pi}

and y = \frac{(360 \sqrt{\pi})}{(2 + \sqrt{\pi})}

Jameson