How do I keep florist bought roses for more than a week?

I'll include a link to a project I posted last year for extending my Mother's Day bouquet. http://www.hometalk.com/diy/grow/plants/how-to-save-a-wilting-bouquet-16397534

I get the packets of preservative from the floral department and add it when I change the water.

I cut them at a slant, change the water. As they get shorter I change the container to a smaller one and looks like a new bouquet.

When you bring the flowers home, be sure to cut the ends on an angle while underwater. Keeping them always in water while you cut doesn't allow air into the stem. The 'air bubble' is what makes the stem weaken. Also use warmer water not cold.

Use warm-lukewarm water in the vase, instead of cold as well- good luck!

Add a small baby aspirin to water and cut stems about 1 inch under running water before putting them back in vase.

oh, now I see what went wrong, I cut the stems out of the water and air probably got to them.