Password problem--never set one up

I have a new macbook. I never set up a password, for either my log in or my husband's. On my log in, if I want to send a picture to the trash, I can do it. When I am in my husband's log in, it asks for an administrator name and password to perform the function. I followed the reset password directions, using the installation disc, but kept our log ins without a password, but creating one for the administrator. Still can't delete photos on his log in, even using "administrator" and the password, and trying my "name" and his, as shown in our user window. What the heck is up?