The question i need help with is as follows:

"If you had $1 million invested in 3-year 5% coupon bonds with FV $100 where YTM=5%, how many 4-year zero-coupon bonds with price $82.27 and FV $100 would you need to short-sell to hedge your interest rate risk?"

As far as i'm aware, to hedge interest rate risk i would need to find the number of zero coupon bonds that ensure the total PV of the coupon bonds are equal to the total PV of the zero coupon bonds, and also have durations of each equal. Please explain how this occurs in the answer so that i can understand it better.

Thank you :)