Pretty sure I got this problem from Math Forum POWS some years ago. It’s fun.

At a recent math conference, lunch was provided for the participants. To be sure that there was enough food for everyone, the kitchen staff made more lunches than there were people attending. In fact, the ratio of prepared lunches to people was 7:5.

Because they anticipated a large number of vegetarians at the conference, the staff made 2 vegetarian lunches for every 3 non-vegetarian lunches.

It turned out that the ratio of non-vegetarians to vegetarians at the conference was 3:4. What was the ratio of vegetarian lunches to vegetarians?

I wrote the problem as a visual for the kids because it helps me too!