Price elasticity of demand is measured by the % change in quantity/the % change in price. With no change in the price of pie, but an increase in the price of sauce, and the fact that we must spend all $20 and no more, we know that we will be buying less sauce AND less pie. That means that the price change in sauce times the quantity change in sauce will equal the change in the quantity of pie times the price of the pie.
Imagine we have Pie at $5 each and Sauce at $1 a bottle. We buy 3 pies and 5 sauce for a total of $20. Sauce goes to $2 a bottle. We have to buy less pie and less sauce to stay at $20.
at first $20 = (5 * 3pies) + (1 * 5sauce)
So $20 now = 5p+2s
I have to buy less pie and less sauce, so I can't just cut my sauce consumption to 2.5 bottles and keep my 3 pies. Since I have to buy less pie than I did before, even though its the same price, that means that I'm going to be buying more sauce that I would ordinarily want to buy based on the price change. the fact that I am buying more sauce than I would otherwise buy in response to the price change means my demand is inelastic by virtue of the fact that the sauce is complimentary with pie.