At a book fair, there were 120 more adults than girls. The number of girls was 75% of the number of boys and 12% of the total number of people. How many adults were there at the book fair?

Sure, let's solve this step by step:

1. Let's denote the number of girls as G, the number of boys as B, and the number of adults as A. From the problem, we know that A = G + 120.

2. We also know that G = 0.75B (since the number of girls was 75% of the number of boys).

3. Additionally, we know that G = 0.12T (since the number of girls was 12% of the total number of people).

4. The total number of people at the book fair is the sum of the number of girls, boys, and adults. So, T = G + B + A.

5. We can substitute G = 0.12T into the equation A = G + 120 to get A = 0.12T + 120.

6. We can also substitute G = 0.75B into the equation T = G + B + A to get T = 0.75B + B + 0.12T + 120.

7. Simplifying the equation from step 6 gives T = 1.75B + 0.12T + 120.

8. Rearranging the equation from step 7 gives 0.88T = 1.75B + 120.

9. We can solve this equation for B to get B = (0.88T - 120) / 1.75.

10. Substituting B = (0.88T - 120) / 1.75 into the equation G = 0.75B gives G = 0.75 * (0.88T - 120) / 1.75.

11. Solving this equation for T gives T = (1.75G + 120) / 0.88.

12. Substituting G = 0.12T into the equation from step 11 gives T = (1.75 * 0.12T + 120) / 0.88.

13. Solving this equation for T gives T = 120 / (0.88 - 1.75 * 0.12).

14. Calculating T gives T = 1000.

15. Substituting T = 1000 into the equation A = 0.12T + 120 gives A = 0.12 * 1000 + 120 = 240.

So, there were 240 adults at the book fair.