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:
[tex]\frac{800}{120}=\frac{100}{x}[/tex]Now you must solve for the variable "x", as following:
[tex]\begin{gathered} (\frac{800}{120})(x)=100 \\ \frac{800}{120}x=100 \\ 800x=100\cdot120 \\ 800x=12,000 \\ x=\frac{12,000}{800} \\ x=15 \end{gathered}[/tex]Therefore, 15 participants out of 100 are running for a cause. The answer is: OPTION D.