Problem with membership contribution page
I was about to suggest the following but found that a Price Field for memberships that is set to Text / Numeric Quantity doesn't allow one to set the Membership type - odd - am digging further but will leave the recipe here for now 

Turn off Contribution Amount on the Amounts tab. 

Create a Price Set set up for Membership and with Min Amount set to $100, make a Price Field of type Text / Numeric Quantity with 1.00 as the unit. 

Turn off Display Amount.

On the membership tab of the Contribution Page select Price Set created above

You should then have a field where you can enter an amount and if it is not above the minimum required will get an outcome like this.