CFAI EOC Reading 38 #9

The question involves selling a 5 year bond and using the proceeds to buy a 10 year while maintaining the dollar duration of the portfolio. I don’t understand the solution, which is to multiply the price/par value * duration * par value * 0.01. This is divided by (the duration of the 10 year * quoted price * .01). This is the par value of the 10-year in order to execute the strategy. Can someone explain in simple engish why you’re doing the calculations? I understand the first step gets you the dollar duration, but that’s about it

A. price/par value * duration * par value * 0.01 = price * duration * 0.01 = price change for a 1% change in interest rate. B. denominator = price * 0.01 * duration => price change of 10 year bond for a 1% price change. if the $ duration has to be the same -> A must be equal to B * How much of B should be bought (B_Val). so how much of B should be bought? B_Val = Numerator / denominator