Hi and Welcome to JA!
The value depends on a lot of things so I need to gather some more information before I help you.
First, are you sure it is ivory??? If so, I'll answer the question assuming it is ivory. If you're not sure, please send a close up photo of any "grain" or "pattern" that you can see.
Second, what does the set look like? Is it carved, plain? If it has a decoration, what is the motif? Here a picture would really help as well.
To send pictures reply to this message. You can attach pictures using the green button to the right of the smiley face (pics must be under 1MB).
Looking forward to your response,
Thank you for the additional information. Since the set is plain and so extensive, it is most likely "french ivory" which is really a plastic/ celluloid made to look like real elephant ivory. These sets were popular in the 1920s and 30s. This makes sense given that it was your grandmothers. A set like yours if french ivory is worth $100-200 retail.
If the pieces are real elephant ivory you would see crosshatching in certain areas (maybe at the ends of the boxes, etc). If really elephant ivory the picture frames, boxes and small containers would be worth $100-200 each. The smaller pieces $40-60 each. As you can see there is a BIG price difference.
It is really difficult for me to tell you definitively whether the set is french ivory or ivory without seeing the pieces in person or getting a really good picture of some sort of pattern (real ivory does have a pattern to it). A test that you can use at home, though, is the hot needle test. If the set is plastic (and not real ivory), it will damage (maybe ruin) the piece you test. What you would do is heat up a needle until the tip is red hot and then try to poke the piece you are testing in a hidden area (the back of something or maybe to a piece that might already be damaged). If the material is celluloid/plastic, the needle will go into it b/c it will melt it. Real elephant ivory will not melt. Another test (less invasive, but trickier) is to run a piece quite a bit and see if it starts to smell like plastic.
In conclusion, your set is most likely french ivory and worth $100-200 retail. If you wanted to sell it you could expect to get 1/2 to 1/4 of the lower range price from a dealer. If you really think it might be real elephant ivory it would be worth taking it to an appraiser in your area who can see the pieces in person.
Please let me know if you have any other questions.
If satisfied with the answer, please accept it as this is the only way that I get compensated for my time and effort.
Very Best Wishes,