Let be "x" the number of participants out of 100 who are running for a cause.
According to the explained in the exercise, of the 800 participants in the marathon, 120 are running to raise money for a cause.
Based on this, you can set up the following proportion:
![(800)/(120)=(100)/(x)](https://img.qammunity.org/2023/formulas/mathematics/college/dhsb0w15bjqcdbedvzv6cmkjy4yjk7df5z.png)
Now you must solve for the variable "x", as following:
![\begin{gathered} ((800)/(120))(x)=100 \\ (800)/(120)x=100 \\ 800x=100\cdot120 \\ 800x=12,000 \\ x=(12,000)/(800) \\ x=15 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/t1v9m25uggvcnrmvoqmyok56hw1bh3q4sc.png)
Therefore, 15 participants out of 100 are running for a cause. The answer is: OPTION D.