Wow, you were spoiled.
$20 in 1960 is equivalent to $211 today.
https://www.usinflationcalculator.com/
For sure, I was spoiled. Dinner was often in Hollywood, CA and the movies may have been at Grauman's Chinese or the Pantages theater on Hollywood Blvd, and sometimes a premier at The Village Theater in Westwood. The $20 was also likely meant to cover my lunches at school plus after school snacks for the week, maybe gas money too. I am not sure.
I did have responsibilities at home like cleaning the pool and keeping up the yard. I do not remember getting an allowance per se. A year or so later when I worked for my dad, he would pay me under the table $25.00 a day.
My parents also bought me a '55 Chevrolet Bel Air convertible in February or March 1960; six months prior to my 16th birthday. I drove illegally using my driver's permit until I got my license. Lucky me, that I was never pulled over by the police. Gasoline was only 25˘ a gallon.
My parents house in Encino. CA cost them a whopping $32,500 in '57. According to Trulia it is valued at $2,816,900, but the future owners added on quite a bit too. It still has the same pool or a new one in the same location. Where the tennis courts are now was a pasture and stable for my horse.
https://www.trulia.com/home/5035-densmore-ave-encino-ca-91436-19981148Times have changed. These days, I feel lucky to get one bag of groceries for $100. One bag! Think of that! Guess this is what happens when you live to be ancient, like me.